Show that solving the equation 3 ²x=4 by taking the common logarithm of each side is equivalent to solving it by taking the logarithm with base 3 of each side.

Answers

Answer 1

The solving of equation 3²x=4 in both the given cases gives the answer x = 0.631.

What exactly is an equation?A mathematical statement composed of two representations joined by an equal sign is known as an equation.3x - 5 = 16 is an example of an equation.We obtain the value for the variable x as x = 7 after solving this equation.

So,

(1) Common logarithm:

2x log 3 = log 4, or 2x(0.47712) = 0.60206When we solve for x, we get 0.95424x = 0.60206, and x = 0.60206/0.95424.x = 0.631

(2) Logarithm with base 3:

2x (log to the base 3 of 3) = (log to the base 3 of 4)This can be reduced to 2x(1) = 2x = (log 4)/log 3 = 1.262.Divide the result by 2 to get x = 0.631

Therefore, the solving of equation 3²x=4 in both the given cases gives the answer x = 0.631.

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Related Questions

some children went for fishing.they caught as many fishes as their number.if they caught 81 fishes altogether.how many children were there?​

Answers

Answer: I think 81

Step-by-step explanation:

It might be a trick question. Because it says they caught as many fish as their number SOOO...

Frankie bought 212 appetizers and he invited 12 people to his party. use compatible numbers to estimate the number of appetizers each guest can have? no links

Answers

The estimate of the number of appetizers per guest is 20

How to estimate the number of appetizers?

The given parameters from the question are:

Number of appetizers = 212

Number of people invited = 12

From the question, we are to make use of compatible numbers

This means that we have the following approximation

Number of appetizers = 200

Number of people invited = 10

Next, we estimate the number of appetizers using

Number of appetizers = Total umber of appetizers/Number of people invited

Substitute the known values in the above equation, so, we have the following representation

Number of appetizers = 200/10

Evaluate

Number of appetizers = 20

Hence, the number of appetizers is 20


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PLS HELP WHY NOBODY ANSWERING ME ?

Answers

Answer:

10×5.6=56 5.6×10=56

Step-by-step explanation:

apple trees 10× 5.6 acres of land = 56 apple trees

Which of the following is an equivalent representation of 5-4 ?

Answers

b^-n = 1/b^n
1/5^4
Raise 5 to the power 4
1/625

Translate the following expression the product of a number and 3 decreased by 5


Answers

F (x ) = 3x-5

Solution :

Expression: An expression is a number, a variable, or a combination of numbers and variables and operation symbols

Education: An equation is made up of two expressions connected by an equal sign.

Product of a number by 3  and decreased by 5

let the number be x

product a number by 3  =3x

number is decreased by 5 = -5

Then,

F (x ) = 3x-5

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The sales tax on a purchased item in a given state is a function of the selling price

Answers

The statement that the sales tax on a good that has been purchased is a function of the selling price in a given state, is TRUE.

How does sales tax relate to the selling price?

The sales tax on an item that is purchased is calculated on the selling price of the item and then added to the item so that the person purchasing the item can pay for the sales tax as well.

Because the sales tax is based on the selling price, it is therefore a function of the selling price with the given state being the percentage of the sales tax.

For instance, a 4% sales tax on a good that is $10 is:

= 4% x 10

= $0.40

This sales tax is based on the selling price and so is a function of it.

Options for the question are:

True False

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Question 3 of 10
Will the answer to the subtraction problem below be odd or even?
9297-9178 = ?
OA. Odd
OB. Even
SUBMIT

Answers

Answer:

Odd

Step-by-step explanation:

9281-9178=119

119 is a Odd number

Given a∥b , and c is not parallel to a or b, which statements must be true? Select each correct answer. Responses m∠1=m∠5 the measure of angle 1 equals the measure of angle 5 m∠5=m∠12 the measure of angle 5 equals the measure of angle 12 m∠4=m∠5 the measure of angle 4 equals the measure of angle 5 m∠7=m∠11

Answers

The correct answers of the statement are as follows;

m∠1=m∠5 the measure of angle 1 equals the measure of angle 5m∠4=m∠5 the measure of angle 4 equals the measure of angle 5

How to find angles in parallel lines?

Line a and b area parallel lines.

c is not parallel to a or b.

When parallel lines are cut by a transversal, angle relationships are formed. The angle relationship includes corresponding angles, alternate angles, vertically opposite angles etc.

Therefore, let's select the correct answer in the options.

m∠1 = m∠5

Therefore, the measure of angle 1 is equals to the measure of angle 5 because they are corresponding angles.

m∠4 = m∠5

Therefore, the measure of angle 4 is equals to the measure of angle 5 because they are alternate angles.

Hence, the correct answers of the statement are as follows;

m∠1=m∠5 the measure of angle 1 equals the measure of angle 5m∠4=m∠5 the measure of angle 4 equals the measure of angle 5

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Can someone help me with this? Acelllus

Answers

im pretty sure that the answer is 15.5

If a toy helicopter is moving at 12 m/s, how much energy does the 3kg toy have?

Answers

The answer would be 216J

Absolute value what is greater |-4.3| or |-7.2|

Answers

Answer:

The absolute value of -7.2 is greater.

Step-by-step explanation:

Absolute value means the distance from zero.  Distance is always measured with a positive number.  Which number is farther from 0, -7.2 or -4.3?  -7.2

Rio has 3/4 liters of milk. He uses 1/3 of the milk to make tea. How much milk does Rio use for the tea?

Answers

Answer:

5/12

I'm assuming this means how much milk is left because it tells how much milk was used in the question

Step-by-step explanation:

Convert to common denominator and you get 9/12 of milk - 4/12 of milk and you get 5/12

What is the expression and value of "six less than the quotient of a number and two, increased by ten" when n = 20? startfraction n over 2 endfraction minus 6 10; when n = 20, the value is 14. 6 minus startfraction n over 2 endfraction 10; when n = 20, the value is 6. startfraction n over 2 endfraction minus 6 10; when n = 20, the value is 17. 6 minus startfraction n over 2 endfraction 10; when n = 20, the value is 3.

Answers

The algebraic expression that represents the expression "six less than the quotient of a number and two, increased by ten" is [(n/2) - 6] + 10 and its value is 14 when n is 20.

An algebraic expression is a number, variable, or the combination of both and operational symbols.

The expression "six less than the quotient of a number and two, increased by ten" can be written as:

[(n/2) - 6] + 10

where n is the number

Evaluate the expression by substituting the value of n.

[(n/2) - 6] + 10

= [(20/2) - 6] + 10

= (10 - 6) + 10

= 4 + 10

= 14

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On a slow weekend, you spend at least two hours on homework. on a busy weekend, you spend as much as five hours on homework. write an absolute value inequality that represents the number of hours you spend doing homework on a typical weekday.

Answers

Absolute value inequality that represents the number of hours you spend doing homework on a typical weekday is 2 ≤ x ≤ 5.

Let us assume that one spends x hours doing homework on a typical weekday. Then we can write

The inequality expression for a slow weekend is given as;

X ≥ 2

In the same vein, the inequality expression for a busy weekend is given as;

X ≤ 5

Putting the two inequalities we have together in the same expression;

2 ≤ x ≤ 5

Two inequality expression could be written simultaneously if they can be expressed individually. They are commonly referred to as a “double” inequality.  Writing an absolute value for this expression is represented as:

|x - h|≤ k

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How to do constant of proportional rate in a graph

Answers

Answer:

the constant of proportionality is the slope


I WILL MARK YOU BRAINLIST IF YOU ANSWER THIS QUESTION FOR ME!!

Answers

you can do this two ways:

1. reflect ABC on the x and y axis, then translate the points up one and three to the right.

2. translate 3 to the left and 1 down and then reflect ABC on the x and y axis.

The 15 members of a team are getting new uniforms. Shirts cost $25
each, shorts cost $30 each, and shoes cost $75 a pair. What is the TOTAL
cost of the new uniforms for ALL of the members?

Answers

Answer:

$1,950.00

Step-by-step explanation:

Total cost of shirts = $25 x 15 = $375

Total cost of shorts = $30 x 15 = $450

Total cost of shoes = $75 x 15 = $1,125

Total cost = $375 + $450 + $1,125

                = $1,950.00

2=2 how to get the answer for this

Answers

Answer:

16 if 8/2(2+2)

Step-by-step explanation:

First take 8 and divide it by 2, and then multiply by 4. This gets to the correct answer of 16.


Solve each equation.
25x =1/5

Answers

The value of x for 25x =1/5 is 0.008

What is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) component are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Given,

25x = 1/5

x = 1/125

x = 0.008

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Since the cookie sheets can hold exactly 1 dozen cookies, bbcc will produce and sell cookies by the dozen. How much time will it take to fill an order of 2, 3, or 4 dozen cookies?

Answers

Time taken to fill an order of 2, 3, 4 dozen cookies are 45 minutes, 64 minutes and 89 minutes respectively.

To calculate time taken to fill the orders, we will add time used in different processes separately.

time taken to spoon =2 min for each dozen

time taken to bake =  10 min for each dozen

time taken to cool = 5 min for each dozen

time taken to pack = 2 min for each dozen

time taken to receive payment = 1 min for each dozen

time for cookies = mins to mix +  mins to spoon +  total baking mins +  mins to cool + mins to pack + min to receive payment

putting the values in the above formula, we get

Cycle time for 2 dozen cookies = 6 mins to mix + 4 mins to spoon + 20 total baking mins + 10 mins to cool + 4 mins to pack + 1 min to receive payment = 45 mins

Cycle time for 3 dozen cookies = 6 mins to mix + 6 mins to spoon + 30 total baking mins + 15 mins to cool + 6 mins to pack + 1 min to receive payment = 64 mins

Cycle time for 4 dozen cookies = 12 mins to mix + 8 mins to spoon + 40 total baking mins + 20 mins to cool + 8 mins to pack + 1 min to receive payment = 89 mins

Therefore, Time taken to fill an order of 2, 3, 4 dozen cookies are 45 minutes, 64 minutes and 89 minutes respectively.

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Anybody know the answer to this question?

Answers

answer a ka gim tul hd shi kdi

pls help with this question attached

Answers

The value of equation P (x) = [tex]2[/tex] + [tex]\frac{x}{2}[/tex] + [tex]x^{2}[/tex] - [tex]\frac{x^{2} }{3}[/tex] when x = (-1) is P(-1) = [tex]\frac{13}{6}[/tex]

P (x) = [tex]2[/tex] + [tex]\frac{x}{2}[/tex] + [tex]x^{2}[/tex] - [tex]\frac{x^{2} }{3}[/tex]

If the value of x = -1

P (-1) = 2 + [tex]\frac{-1}{2}[/tex] + [tex](-1)^{2}[/tex] - [tex]\frac{(-1)^{2} }{3}[/tex]

P (-1) = 2 - [tex]\frac{1}{2}[/tex] + 1 - [tex]\frac{1}{3}[/tex]

The above equation consist of fractional numbers as well as the whole numbers to therefore it is not possible to apply the operations in this particular conditions.

Equation is statement which equates two algebraic expressions.

On taking LCM for the denominators of the fractional numbers (2 , 3), we get 6 as the Least Common Multiple.

To apply the sum and difference operation, we need to make the denominators of all the terms same.

[tex]2 * \frac{6}{6} = \frac{12}{6}[/tex][tex]\frac{1}{2} * \frac{3}{3} = \frac{3}{6}[/tex][tex]1 * \frac{6}{6} = \frac{6}{6}[/tex][tex]\frac{1}{3} * \frac{2}{2} = \frac{2}{6}[/tex]

P (-1) = [tex]\frac{12}{6} - \frac{3}{6} + \frac{6}{6} - \frac{2}{6}[/tex]

P (-1) = [tex]\frac{12-3+6-2}{6}[/tex]

P (-1) = [tex]\frac{13}{6}[/tex]

Value of the equation P when 'x' is replaced by (-1) will be [tex]\frac{13}{6}[/tex]

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whats the gcf of 11 and 19?​

Answers

Answer:

1

Step-by-step explanation:

The greatest common factor (GCF) of 11 and 19 would = 1

10 pts + brainliest
help pleasee
(science)

Answers

The mass number of the atom is 4.

How to find the mass number of an atom?

The mass number, also called atomic mass number or nucleon number, is the total number of protons and neutrons (together known as nucleons) in an atomic nucleus.

Therefore, the sum of protons and neutron in the nucleus of an atom is mass number of that atom.

Therefore, the atoms in the diagram has 2 electrons, 2 protons and 2 neutrons.

Notice the electrons revolving around the nucleus of an atom.

Therefore,

mass number = mass of neutron + mass of proton

mass number = 2 + 2

mass number = 4

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What is −11 + |−5| − |−15|?

HELP NOW PLS!!!
I WILL MARK YOU BRAINLIEST

Answers

-21
The answer for this questions would be -21

Round to the nearest ten, then estimate the product. 46 x 63 =_ O 2,400 O2,800 O 3,000 0-3,500​

Answers

The product of 46 and 63 to the nearest ten is 3000

What is the product?

Product is the result of the multiplication process. Multiplication is the mathematical operation where a number a number is added to another number repeatedly. The sign that represents multiplication is x.

In order to round to the nearest ten, if the unit digit is greater than 5 or equal to 5, 1 is the added to the tens digit and the unit digit becomes zero. If the unit digit is less than 5, there is no change in the tens digit and the unit digit becomes zero.

46 to the nearest ten becomes 50

63  to the nearest ten becomes 60

50 x 60 = 3000

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The product of  46 x 63 when it is been rounded off into the nearest ten can be written as 3,000.

What is Rounding Off?

Rounding off  can be described as the mathematical term of making a particular number to become simpler even though the value of that number is still intact .

From the question,  product of ( 46 x 63 )  will give us 3,818. however this number can be rounded off, to tens which will now give us 3,000 because it is tens the first two number from the right has been rounded off.

Therefore, option C is correct.

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Do y’all need any help

Answers

Answer:

Yes

Step-by-step explanation:

Math, due tomorrow and i can't find the rate of enlargement of my dilation in transformation....

During one month Andre used 785 gallons of water at his home. There are approximately 3.8 liters in 1 gallon.Which measurement is closest to the number of liters Andre used during this month?

Answers

The closest measurement to the number of liters Andre used during the month is 2,983 liters of water.

How is the measurement determined?

The measurement of the number of liters used is determined by multiplying the number of gallons of water by the approximate value of 1 gallon in liters.

Using one of the mathematical operations, multiplication, the conversion of the quantity of water from gallons to liters can be computed.

Data and Calculations:

The total number of gallons of water used = 785

Conversion of 1 gallon to liters = 3.8 liters per gallon

The total number of liters of water used = 2,983 (785 x 3.8)

Thus, the closest measurement to the number of liters Andre used during the month is 2,983 liters of water.

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Answer:

The answer is 2,983

Step-by-step explanation:

Please answer this question.

Answers

Answer:

I have attached as an image. Kindly check.

Step-by-step explanation:

Graph the function y equals 12 times the quantity 1 over 3 end quantity to the x power. Does the function represent growth or decay? What is the equation of the asymptote?

Answers

Exponential equation are inverse of of the logarithmic equation. Since b = 1/3 which is less than 1, hence it is a decay.

Exponential equation

Exponential equation are inverse of of the logarithmic equation. The standard exponential equation is y= ab^x

Exponential equation can either be growth or decay depending on the rate constant value.

If the value of b < 1, it is a decay while if the value of b > 1, then it is growth. Given the exponential equation below;

y = 12(1/3)^x

Since b = 1/3 which is less than 1, hence it is a decay. Find the graph attached.

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Answer:

D.    Decay; y = 0

Step-by-step explanation:

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