Answer:
[tex]a = \frac{1}{134217728}[/tex]
Step-by-step explanation:
Given
[tex]8^x = a^{-x/9}[/tex]
Required
Find a
Take log of both sides
[tex]log(8^x) = log(a^{-x/9})[/tex]
Apply law of logarithm
[tex]x\ log(8) = (-x/9) log(a)[/tex]
Divide both sides by a
[tex]log(8) = -\frac{1}{9} log(a)[/tex]
Multiply both sides by -9
[tex]-9\ log(8) = log(a)[/tex]
Apply law of logarithm
[tex]log(8^{-9}) = log(a)[/tex]
Cancel out log
[tex]8^{-9} = a[/tex]
Rewrite as:
[tex]a = 8^{-9}[/tex]
Apply law of indices
[tex]a = \frac{1}{8^9}[/tex]
[tex]a = \frac{1}{134217728}[/tex]
