Question

Help two questions only!!!!

Answer 1

1)
`9^(2)=81`

2)
`7=log_(2)(128)`

Explanation:

1)

We need to use the property of power and logarithms, particularly this:

`a=x^{log_(x)(a)}` (1)

So, let's take take the exponent:

`9^{log_(9)}((1)/(81))=9^(-2)`

`(1)/(81)=9^(-2)`

now, we can write the negavitve power as:

`(1)/(81)=(1)/(9^(2))`

So, the aswer will be:

`9^(2)=81`

2)

Applying equation 1, let's take log in base 2 on each side of the equation

`log_(2)(2^(7))=log_(2)(128)`

using the power definition in log, we have:

`7log_(2)(2)=log_(2)(128)`

Therefore, the answer is:

`7=log_(2)(128)`

I hope it helps you!