Question

solve. write your answer in simplest form using integers, fractions, and common logarithms.
3 = 4^x
x =

Explanation:

Step1: Take log of both sides

Take the common logarithm (base 10) of both sides of the equation \(3 = 4^{x}\). So we get \(\log(3)=\log(4^{x})\).

Step2: Use logarithm power rule

Using the power rule of logarithms \(\log(a^{b}) = b\log(a)\), the right - hand side becomes \(x\log(4)\). So the equation is \(\log(3)=x\log(4)\).

Step3: Solve for x

To solve for \(x\), divide both sides of the equation by \(\log(4)\). We have \(x=\frac{\log(3)}{\log(4)}\).

Answer:

\(\frac{\log(3)}{\log(4)}\)