## Precalculus: Mathematics for Calculus, 7th Edition

$\log{e} = \dfrac{1}{\log_e{10}}$ Refer to the step-by-step answer for the solution.
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: $\log{e} = \dfrac{1}{\log_e{10}}$