Answer
$\displaystyle \{\frac{\log 0.3+\log 1.7}{2\log 1.7 -\log 0.3}\}$ or $\{-0.297\}$
Work Step by Step
... Apply $\log$(...) to both sides and isolate x
$\log 0.3^{1+x}=\log 1.7^{2x-1}$
$(1+x)\log 0.3=(2x-1)\log 1.7$
$\log 0.3+x\log 0.3=2x\log 1.7-\log 1.7$
$\log 0.3+\log 1.7=2x\log 1.7 -x\log 0.3$
$\log 0.3+\log 1.7=x(2\log 1.7 -\log 0.3)$
$x=\displaystyle \frac{\log 0.3+\log 1.7}{2\log 1.7 -\log 0.3}\approx-0.297$
The solution set is $\displaystyle \{\frac{\log 0.3+\log 1.7}{2\log 1.7 -\log 0.3}\}$ or $\{-0.297\}$
