Answer
a = 6x
Explanation
We are asked to solve for a, and express it in terms of x.
To do this, we will use two of the Laws of Logarithms
log dᶜ = c log d
logₐb = (log b)/(log a)
So, for this question,
[tex]\begin{gathered} \log _{4^x}2^a \\ =a\log _{4^x}2 \\ \text{But we know that} \\ \log _{4^x}2=\frac{\log2}{\log4^x} \\ a\log _{4^x}2=\frac{a\log2}{\log4^x} \\ So,\text{ the original equation} \\ \log _{4^x}2^a=3 \\ \frac{a\log2}{\log4^x}=3 \\ \text{Cross multiply} \\ a\log 2=3\log 4^x \\ \text{Divide both sides by log 2} \\ a=\frac{3\log4^x}{\log2} \\ a=\frac{3\log4^x}{\log2}=\frac{3x\log4}{\log2}=\frac{3x\log2^2}{\log2}=\frac{6x\log 2}{\log 2}=6x \end{gathered}[/tex]
Hope this Helps!!!
