Chapter 4, Exponential and Logarithmic Functions - Section 4.5 - Exponential and Logarithmic Functions - 4.5 Exercises - Page 404: 34

(a) $x=\frac{1}{\log 6+1}$ (b) $x\approx 0.562382$

(a) We need to solve: $10^{1-x}=6^{x}$ We take the log of both sides and use log rules to simplify: $\log 10^{1-x}=\log 6^{x}$ $1-x=x(\log 6)$ $1=x(\log 6)+x$ $1=x(\log 6+1)$ $x=\frac{1}{\log 6+1}$ (b) We solve using a calculator: $x\approx 0.562382$