Question

Solve the following equations, having given $\log 2,\log 3$, and $\log 7$.
$3^{x-1}=5$.

Answer 1

$3^{x-1}=5$

Applying $\log$ on both the sides, we get

$(x-1)\log 3=\log 5$

$\Rightarrow x=\frac{\log 5+\log 3}{\log 3}$

$\Rightarrow x=\frac{1-\log 2+\log 3}{\log 3}\Rightarrow x=2.4649733$