Question

What is the value of a when we rewrite 8^x as a^-x/9​

Answer 1

`a = (1)/(134217728)`

Explanation:

Given

`8^x = a^(-x/9)`

Required

Find a

Take log of both sides

`log(8^x) = log(a^(-x/9))`

Apply law of logarithm

`x\ log(8) = (-x/9) log(a)`

Divide both sides by a

`log(8) = -(1)/(9) log(a)`

Multiply both sides by -9

`-9\ log(8) = log(a)`

Apply law of logarithm

`log(8^(-9)) = log(a)`

Cancel out log

`8^(-9) = a`

Rewrite as:

`a = 8^(-9)`

Apply law of indices

`a = (1)/(8^9)`

`a = (1)/(134217728)`