Question

Im having trouble on this practice problem, please help me step-by-step.* In the picture provided, solve the equation for a.Express your answer in terms of x. *

Answer 1

`a=\log _24^(3x)`

1) In this logarithm we can notice there are two variables. Let's rewrite it by applying the definition for Logarithm:

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

2) Now to solve for a, we need to perform some logarithm manipulation:

`\begin{gathered} \log _22^a=\log _24^(3x) \\ a\cdot\log _22=\log _24^(3x) \\ a\cdot1=\log _24^(3x) \\ a=\log _24^(3x) \end{gathered}`

Note here, the application of logarithm of a power "dropping" the exponent in front of the logarithm expression and rewriting it as a factor.

3) Hence, the answer is:

`a=\log _24^(3x)`