Question

If $\log 2=0.30103$, then solve $2^x=25$.

Answer 1

$2^x=25$

Take log both sides,

$\log 2^x=\log 25$

$x\log 2=\log 5^2$

$x\log 2=2\log 5$

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

$x\log 2=2(\log 10-\log 2)$

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

$x=\frac{2}{\log 2}-2$

$x=\frac{2}{0.30103}-2$

$x\approx 6.644-2$

$x\approx 4.644$