Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 7 - Exponential and Logarithmic Functions - 7-6 Natural Logarithms - Practice and Problem-Solving Exercises - Page 481: 17

Answer

$\ln{40,960}$

Work Step by Step

Recall: (1) $n\cdot \ln{a}=\ln{a^n}$ (2) $\ln{a}+\ln{b}=\ln{(ab)}$ (3) $\ln{a}-\ln{b} = \ln{\left(\frac{a}{b}\right)}$ Use rule (1) above to obtain: \begin{align*} &=\ln{\left(8^4\right)}+\ln{10}\\ &=\ln{4096}+\ln{10} \end{align*} Use rule (2) above to obtain: \begin{align*} &=\ln{(4096\cdot 10)}\\ &=\ln{40,960} \end{align*}
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