## College Algebra (10th Edition)

$\displaystyle \{\frac{\log 3}{\log 36}\}$ or $\{0.307\}$
... Apply $\log$(...) to both sides $\log 3^{1-2x}=\log 4^{x}$ $\quad$...Apply$: \quad \log_{a}M^{r}=r\log_{a}M\quad$ $(1-2x)\log 3=x\log 4 \quad$... isolate x $\log 3-2x\log 3=x\log 4$ $\log 3=x\log 4+2x\log 3$ $\log 3=x(\log 4+2\log 3) \quad$...Apply$: \quad \log_{a}M^{r}=r\log_{a}M\quad$ $\log 3=x(\log 4+\log 9) \quad$...Apply$: \quad \log_{a}(MN)=\log_{a}M+\log_{a}N$ $\log 3=x(\log 36)$ $x=\displaystyle \frac{\log 3}{\log 36}\approx 0.307$ Solution set: $\displaystyle \{\frac{\log 3}{\log 36}\}$ or $\{0.307\}$