Chapter 4, Exponential and Logarithmic Functions - Section 4.5 - Exponential and Logarithmic Functions - 4.5 Exercises - Page 404: 15

(a) $x=1-\frac{\log 3}{\log 2}$ (b) $x\approx-0.584963$

(a) We need to solve: $2^{1-x}=3 $ We take the log of both sides and use log rules to simplify: $\log 2^{1-x}=\log 3$ $(1-x)\log 2=\log 3$ $1-x=\frac{\log 3}{\log 2}$ $x=1-\frac{\log 3}{\log 2}$ (b) We use a calculator: $x\approx-0.584963$