Question

If $log2=0.3010$ and $3=0.4771$, the value of $lo{g}_{5}512$ is

• A. 2.87
• B. 2.967
• C. 3.876
• D. 3.912

Answer 1

The correct option is C 3.876

$lo{g}_{5}512=\frac{log512}{log5}$
$=\frac{log{2}^9}{log\left(10/2\right)}$
$=\frac{9log2}{log10-log2}$
$=\frac{9\times 0.3010}{1-0.3010}$
$=\frac{2.709}{0.699}$
$=\frac{2709}{699}$
$=3.876$