Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 4 - Review - Concept Check - Page 388: 9

Answer

Please see step-by -step.

Work Step by Step

a. An exponential equation is an equation in which the unknown (variable) appears in the exponent. b. Guidelines for Solving Exponential Equations can be found on p. 361. 1. Isolate the exponential term on one side of the equation. 2. Take the logarithm of each side, and use the Laws of Logarithms to ``bring down the exponent.'' 3. Solve for the variable. $c.$ Following the plan outlayed in part b, 1. The exponential term is already isolated on the LHS. 2. take the logarithm of both sides, and use the law $\quad \log_{a}(A^{c})=C\log_{a}A$: $\log 2^{x}=\log 19$ $x\log 2=\log 19\quad/\div\log 2$ ( ...3. solving for x) $x=\displaystyle \frac{\log 19}{\log 2}\approx $4.24792751344
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