Question

How would I solve this equation: e^3x=10

Answer 1

\[e^{3x}=10\\
3x=\ln(10)\] is the first step

Answer 2

another way to explain, may be this, by definition of logarithm we can write:
\[10=e ^{\ln 10}\]
so your equation can be rewritten as below:
\[e ^{3x}=e ^{\ln(10)}\]
now equating the exponents each other, we can write:
\[3x=\ln(10)\]

Answer 3

subsequently, please divide both sides of that equation, by three, and you will get:
\[x=\frac{ \ln 10 }{ 3 }\]

Answer 4

please note that:
\[\ln 10=\log _{e}10\]