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`