Question

Solve the equation for aExpress your answer in terms of x

Answer 1

a = 6x

Step-by-step 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,

`\begin{gathered} \log _(4^x)2^a \\ =a\log _(4^x)2 \\ \text{But we know that} \\ \log _(4^x)2=(\log2)/(\log4^x) \\ a\log _(4^x)2=(a\log2)/(\log4^x) \\ So,\text{ the original equation} \\ \log _(4^x)2^a=3 \\ (a\log2)/(\log4^x)=3 \\ \text{Cross multiply} \\ a\log 2=3\log 4^x \\ \text{Divide both sides by log 2} \\ a=(3\log4^x)/(\log2) \\ a=(3\log4^x)/(\log2)=(3x\log4)/(\log2)=(3x\log2^2)/(\log2)=(6x\log 2)/(\log 2)=6x \end{gathered}`

Hope this Helps!!!