Question

Solve the following equations:
$\frac{a^{x+1}}{b^{x-1}}=c^{2x}$.

Answer 1

$\frac{a^{x+1}}{b^{x-1}}=c^{2x}$

Applying $\log$ on both the sides gives

$\log \left(\frac{a^{x+1}}{b^{x-1}}\right)={\log (c}^{2x})\Rightarrow (x+1)\log a-(x-1)\log b=2x\log c\Rightarrow x(\log a-\log b-2\log c)=-\log a-\log b\Rightarrow x=\frac{\log a+\log b}{\log b+2\log c-\log a}$