Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 7 Exponential and Logarithmic Functions - 7.6 Solve Exponential and Logarithmic Equations - Guided Practice for Examples 2 and 3 - Page 516: 6


$$x=-\frac{10\ln \left(5\right)}{3}$$

Work Step by Step

Since there is a variable in the exponent on one side of the equation, we use logarithms/natural logarithims. Doing this, we find: $$e^{-0.3x}=5 \\ \ln \left(e^{-0.3x}\right)=\ln \left(5\right) \\ -0.3x=\ln \left(5\right) \\ x=-\frac{10\ln \left(5\right)}{3}$$
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