Answer
$\log{e} = \dfrac{1}{\log_e{10}}$
Refer to the step-by-step answer for the solution.
Work Step by Step
RECALL:
The change-of-base formula for loagarithms:
$\log_b{x} = \dfrac{\log_a{x}}{\log_a{b}}$
Note that a $\log{}$ without a specified base means that the base is 10.
Using the change-of-base formula with $a=e$ gives:
$\log{e} = \dfrac{\log_e{e}}{\log_e{10}}$
Since $\ln{e} = 1$, then the expression above is equivalent to:
$\log{e} = \dfrac{1}{\log_e{10}}$
