Question

I need help on this practice problem Solve the equation for a.Express your answer in terms of x

Answer 1

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

The first thing we have to do is eliminate the logarithm. For that we raise the base of it on both sides

$\begin{gathered} (4^x)^{log(2)}=(4^x)^3 \\ 2^a=4^{3x} \end{gathered}$

To solve for a we must take logarithm in base 2 to both sides of the equality

$log_2(2^a)=log_2(4^{3x})$

Since 4 = 2x2 we can write what is inside the log in terms of 2 to lower the exponent

$a=log_2(2^{6x})$

And now we can eliminate the logarithm and we are left with the final answer

$a=6x$