Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Section 4.4 - Laws of Logarithms - 4.4 exercises - Page 359: 69


$\log{e} = \dfrac{1}{\log_e{10}}$ 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: $\log{e} = \dfrac{1}{\log_e{10}}$
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