Precalculus (6th Edition) Blitzer

Solution set = $\{0.01,10^{3/2}\}$
The equation is defined only for $x\gt 0$. Temporarily, substitute $t=\log x$. We have $t(2t+1)=6$ $2t^{2}+t-6=0$ Factor by finding two factors of $2(-6)=-12$ with a sum of 1. We find -3 and +4. Rewrite and factor in pairs. $2t^{2}+4t-3t-6=0$ $2t(t+2)-3(t+2)=0$ $(t+2)(2t-3)=0$ $\left[\begin{array}{lll} t=-2\Rightarrow & \log x=-2\Rightarrow & x=10^{-2}=0.01\\ or & & \\ t=3/2\Rightarrow & \log x=3/2\Rightarrow & x=10^{3/2}\approx 31.62 \end{array}\right]$ Solution set = $\{0.01,10^{3/2}\}$ Check graphically: