Question

Solve the following equations, having given $\log 2,\log 3$, and $\log 7$.
$5^x={10}^3$.

Answer 1

$5^x={10}^3$

Taking logarithm on both sides

$\Rightarrow x\log 5=3\log 10$

$\Rightarrow x\log \frac{10}{2}=3$

$\Rightarrow x(1-\log 2)=3$

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