Question

If log 2 = 0.3010 and log 3 = 0.4771, the value of $lo{g}_{5}512$ is:

• A. 2.870
• B. 2.967
• C. 3.876
• D. 3.912

Answer 1

The correct option is C

3.876

$lo{g}_{5}512=\frac{log512}{log5}$

$=\frac{log{2}^9}{log\left(\frac{10}{2}\right)}$

$=\frac{9log2}{log10-log2}$

$=\frac{9\times 0.3010}{1-0.3010}$

$=\frac{2.709}{0.699}$

$=3.876$