Question

solve the logarithmic equation: 10^(2x+5)=e

Answer 1

\[\ln 2x+5=10\]

Answer 2

\[
10^{2x+5}=e
\]
to bring th exponent down, we take the logarithm to that base\[
\log_{10}10^{2x+5}=\log_{10}e\\
(2x+5)\log_{10}10=\log_{10}e\\
{\rm property:}\quad\log_aa=1\\
(2x+5)(1)=\log_{10}e\\
2x=\log_{10}(e)-5\\
\vdots
\]