Question

Solve the logarithmic equation. Round to the nearest ten-thousandth if necessary.
\[ 3 \log (2x) = 4 \]

Answer 1

3 log(2x) = 4
log(2x) = 4/3
2x = 10^(4/3)
x = (1/2) 10^(4/3)

Answer 2

What log properties did you use?

Answer 3

\(\bf 3log(2x)=4\implies 3log_{10}(2x)=4\implies log_{10}(2x)=\cfrac{4}{3}\\ \quad \\
\textit{log cancellation rule of }\qquad \Large \color{red}{a^{log_ax}=x}\qquad thus\\ \quad \\
log_{10}(2x)=\cfrac{4}{3}\implies \Large 10^{log_{10}(2x)}=10^{\frac{4}{3}}\implies 2x=10^{\frac{4}{3}}\)