Math Grade 8, fractional indicesHi, i am having trouble with the following questions from the lesson fractional indices, please answer with all steps. thanks.  Find the value of x: 1) 4^x = 64 2)...

Math Grade 8, fractional indices

Hi, i am having trouble with the following questions from the lesson fractional indices, please answer with all steps. thanks. 

Find the value of x:

1) 4^x = 64

2) x^2 = 4/9

Please answer them based on the method i have learnt, which is like this: the following is an example, and i would like to learn it the same way. 

16^1/4 = 4 sqrt16 = 2 

 

Asked on by moeenmoeen

2 Answers | Add Yours

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to solve for x the equation `4^x = 64` , hence, since `64 = 4*4*4 = 4^3` , you may substitute `4^3`  for 64 such that:

`4^x =4^3 `

Since the left and right sides are equal, hence, you need to equate the exponents such that:

`x = 3`

Hence, evaluating the solution to the equation `4^x = 64 ` yields`x = 3` .

You need to solve for x the equation `x^2 = 4/9` , hence, you need to raise both sides to the power `1/2`  such that:

`(x^2)^(1/2) = (4/9)^(1/2) `

Using the exponents properties and converting the rational power into a radical yields:

`(x)^(2*1/2) = +-sqrt(4/9) => x_(1,2) = +-2/3`

Hence, evaluating the solutions to the equation `x^2 = 4/9`  yields `x_(1,2) = +-2/3` .

Sameera W's profile pic

Sameera W | (Level 1) eNoter

Posted on

4^x = 64

taking x sqrt both sides

x sqrt(4^x)= x sqrt(64)

(4^x)^(1/x)=(64)^(1/x)

4=(4.4.4)^(1/x)

4=(4^3)^(1/x)

when only x=3, left hand side and right hand side become similar, so the answer is x=3

similarly, x^2=4/9 can be solve

2 sqrt (x^2)=2 sqrt (4/9)

x=(2sqrt(4))/(2sqrt(9))

x=2/3

so the answer is 2/3

 

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