Question

Solve for x:
e^3x=10

Answer 1

\(\large {\bf e^3x=10\implies log_{\color{brown}{ e}}({\color{brown}{ e}}^{3x})=log_{\color{brown}{ e}}10
\\ \quad \\
\textit{use the log cancellation rule of }log_{\color{brown}{ a}}{\color{brown}{ a}}^x=x }\)

Answer 2

\[
10 = e^{\ln(10)}
\]

Answer 3

take logs of each side
3x log(base e) e = log (base e) 10
3x = ln 10
x = ( ln 10) / 3