Question

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

Answer 1

Answer:

$a = \frac{1}{134217728}$

Step-by-step 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

$log(8) = -\frac{1}{9} log(a)$

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

$a = \frac{1}{8^9}$

$a = \frac{1}{134217728}$