# Chapter 4, Exponential and Logarithmic Functions - Section 4.5 - Exponential and Logarithmic Functions - 4.5 Exercises - Page 404: 22

(a) $x=-\frac{1}{5}(\ln 16-3)$ (b) $x\approx 0.045482$

#### Work Step by Step

(a) We need to solve: $e^{3-5x}=16$ We take the natural log of both sides and use log rules to simplify: $3-5x \ln e=\ln 16$ $3-5x=\ln 16$ $-5x=\ln 16-3$ $x=-\frac{1}{5}(\ln 16-3)$ (b) We use a calculator to solve: $x\approx 0.045482$

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