College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 4 - Exponential and Logarithmic Functions - Concept and Vocabulary Check: 7

Answer

fill the blank with $\ln 5$

Work Step by Step

Apply the basic property of logarithms: $ b^{\log_{b}x}=x\qquad$ with base b=e, and substitute x with $5^x$: $5^{x}=e^{\ln 5^{x}}$ $....$and now, apply the The Power Rule: $\log_{\mathrm{b}}\mathrm{M}^{\mathrm{p}}=\mathrm{p}\log_{\mathrm{b}}\mathrm{M}$ $5^{x}=e^{(\ln 5)\cdot x}$ So $y=3\cdot e^{(\ln 5)\cdot x}$ fill the blank with $\ln 5$
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