Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 4 - Exponential and Logarithmic Functions - Section 4.6 Logarithmic and Exponential Equations - 4.6 Assess Your Understanding - Page 337: 43


$\text{Exact: }\dfrac{\ln 10}{\ln 2}$ $\text{Approximately: } 3.322$

Work Step by Step

Note that $a^y = b \text{ is equivalent to } y = \log_a b$. Thus, $2^{x}=10 \longrightarrow x = \log_2 10$ Recall: Change of Base Formula: $\hspace{20pt} \log_ a M = \dfrac{\log_b M}{\log_b a}$ Therefore, $x=\log_2 10 \\\\ x = \boxed{\dfrac{\ln 10}{\ln 2} \approx 3.322}$
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