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 358: 6


(a) $10$; $e$; change-of-base $\log{12}$; $\log{7}$; $1.2770$ (b) yes

Work Step by Step

RECALL: The change-of-base formula for logarithms: $\log_a{b} = \dfrac{\log{b}}{\log{a}}$ This formula works for any base Most calculators can compute logarithms with base $10$ and base $e$. In using a calculator to evaluate logarithms with base other than $10$ and $e$, the change -of-base formula above will be used. (a) Therefore, the missing expressions in the given statement (in order) are: $10$; $e$; change-of-base $\log{12}$; $\log{7}$; $1.2770$ (b) The change-of-base formula will give the same answer even if different bases are used. Thus, using $\ln{}$ in place of $\log{}$ will give the same answer.
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