Question

I need help on this logarithmic equation I need it solved step by step * It asks to solve it in terms of x. *

Answer 1

To solve the function in terms of x:

$\log _{4^x}2^a=3$

find the power of the subscripts of the log

$\begin{gathered} \log _{4^x}2^a=3 \\ \log _{2^{2x}}2^a=3 \\ \frac{a}{2x}\log _22=3 \\ \text{where }\log _22=1 \\ \frac{a}{2x}=3 \end{gathered}$

cross multiply the expression

$\begin{gathered} \frac{a}{2x}=3 \\ a=3(2x) \\ a=6x \end{gathered}$

Therefore the correct answer of a = 6x