Question

Simplify: $\frac{\log 49\sqrt{7}+\log 25\sqrt{5}-\log 4\sqrt{2}}{\log 17.5}$.

• A. $5$
• B. $2$
• C. $\frac{5}{2}$
• D. $\frac{3}{2}$

Answer 1

The correct option is C $\frac{5}{2}$

$\frac{log49\sqrt{7}+log25\sqrt{5}-log4\sqrt{2}}{log17.5}=\frac{log{7}^2{.7}^{1/2}+log{5}^2{.5}^{1/2}-log{2}^2{.2}^{1/2}}{log\frac{175}{10}}$

$=\frac{log{7}^{5/2}+log{5}^{5/2}-log{2}^{5/2}}{log35/2}$

$=\frac{5}{2}\frac{[log7+log5-log2]}{log35/2}=\frac{5}{2}.\frac{log\frac{35}{2}}{log35/2}$

$=\frac{5}{2}$