Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$x \approx - 0.297$
Recall the logarithmic property: $\log m^n= n \log m$ To find the value of $x$, we apply $\log$ to both sides and then isolate $x$ as follows: $\log 0.3^{1+x}=\log 1.7^{2x-1} \\ (1+x)\log 0.3=(2x-1)\log 1.7 \\ \log 0.3+x\log 0.3=2x\log 1.7-\log 1.7 \\ \log 0.3+\log 1.7=x(2\log 1.7 -\log 0.3)$ or, $x=\displaystyle \frac{\log 0.3+\log 1.7}{2\log 1.7 -\log 0.3}\approx - 0.297$ Thus, our answer is: $x \approx - 0.297$