Chapter 4, Exponential and Logarithmic Functions - Section 4.5 - Exponential and Logarithmic Functions - 4.5 Exercises - Page 404: 24

(a) $x=\frac{\log 34}{3\log 2}$ (b) $x\approx 1.695821$

(a) We need to solve: $2^{3x}=34$ We take the log of both sides and use log rules to simplify: $\log 2^{3x}=\log 34$ $3x \log2 = \log 34$ $3x=\frac{\log 34}{\log 2}$ $x=\frac{\log 34}{3\log 2}$ (b) We solve using a calculator: $x\approx 1.695821$