Question

solve 5e^2x=30

Answer 1

\[\Large e^{2x} = \frac{30}{5}\]
\[\Large 2x = \log_e 6\]

Answer 2

\[5e^{2x}=30\]\[e^{2x}=6\]\[\ln e^{2x}=\ln6\]\[2x\ln e=\ln6\]\[2x=\ln6\]\[x=\frac 12
\ln 6\]\[x=\ln6^{1/2}\]\[x=\ln\sqrt{6}\]\[x=\ln\sqrt2+\ln\sqrt3\]