Question

solve. write your answer in simplest form using integers, fractions, and common logarithms.
$7 = 6^{x}$
$x = $

Explanation:

Step1: Take log of both sides

Take the common logarithm (base 10) of both sides of the equation \(7 = 6^{x}\). So we have \(\log(7)=\log(6^{x})\).

Step2: Use logarithm power rule

Using the power rule of logarithms \(\log(a^{b}) = b\log(a)\), the right - hand side becomes \(x\log(6)\). So the equation is now \(\log(7)=x\log(6)\).

Step3: Solve for x

To solve for \(x\), divide both sides of the equation \(\log(7)=x\log(6)\) by \(\log(6)\). We get \(x = \frac{\log(7)}{\log(6)}\).

Answer:

\(\frac{\log(7)}{\log(6)}\)