Question

For each sentence below, find the value of x that makes each sentence true.

(5 ^1/5) ^5 = 25^x x = ____^a0
(8 ^1/3) ^2 = 4^ x x = ____ ^a1

Answer 1

It's 1/2 and then 1

Explanation:

The answer above should have a 5-strar rating. I chose 1/2 and 1 as the answer and I got it right.

Hope I helped:)

Have a great day!!!

Answer 2

1.
`x=(1)/(2)`

2.
`x=1`

QUESTION 1

The first sentence is
`(5^{(1)/(5)})^5=25^x`.

Recall that;

`(a^m)^n=a^(mn)`

We simplify the left hand side by applying this property to get;

`5^{(1)/(5)* 5}=25^x`.

`\Rightarrow 5^(1)=25^x`.

We now rewrite the right hand side too in an index form to obtain;

`\Rightarrow 5^(1)=5^(2x)`

We now equate the exponents to get;

`\Rightarrow 1=2x`.

`\Rightarrow (1)/(2)=x`

`\Rightarrow x=(1)/(2)`.

QUESTION 2

The second sentence is
`(8^{(1)/(3)})^2=4^x`

We simplify the left hand side first to get;

`(2^{3* (1)/(3)})^2=4^x`

`2^2=4^x`

We now rewrite the left hand side too in index form to obtain;

`2^2=2^(2x)`

We equate the exponents to get;

`2=2x`

This implies that;

`1=x`

or

`x=1`