Question

Evaluate $lo{g}_{16}^{32}$ - $lo{g}_{25}^{125}$ + $lo{g}_9^{27}$

• A. 1$\frac{1}{4}$
• B. $\frac{1}{4}$
• C. 1$\frac{1}{3}$
• D. 1$\frac{1}{5}$

Answer 1

The correct option is A

1$\frac{1}{4}$

$lo{g}_{16}^{32}$ - $lo{g}_{25}^{125}$ + $lo{g}_9^{27}$

= $\frac{log32}{log16}-\frac{log125}{log25}+\frac{log27}{log9}$

= $\frac{log{2}^5}{log{2}^4}-\frac{log{5}^3}{log{5}^2}+\frac{log{3}^3}{log{3}^2}$

= $\frac{5log2}{4log2}-\frac{3log5}{2log5}+\frac{3log3}{2log3}$

=$\frac{5}{4}-\frac{3}{2}+\frac{3}{2}$ = $\frac{5}{4}$ = 1$\frac{1}{4}$