## College Algebra (10th Edition)

$\{1+\sqrt[3]{2}\}$ or $\{2.260\}$
(*) For the equation to be defined, it must be true that $x \gt 1$ ...Apply$: \quad \log_{a}M^{r}=r\log_{a}M\quad$ $\log(x-1)=\log 2^{1/3}$ ...Apply$: \quad$If $\log_{a}M=\log_{a}N,$ then $M=N$ $x-1=2^{1/3}$ $x=1+\sqrt[3]{2}\approx 2.25992$ The solution satisfies (*), so the solution set is $\{1+\sqrt[3]{2}\}$ or $\{2.260\}$