Evaluate $l o g_{16}^{32}$ - $l o g_{25}^{125}$ + $l o g_{9}^{27}$ .

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Solution

$l o g_{16}^{32}$ - $l o g_{25}^{125}$ + $l o g_{9}^{27}$

= $\frac{l o g 32}{l o g 16} - \frac{l o g 125}{l o g 25} + \frac{l o g 27}{l o g 9}$

= $\frac{l o g 2^{5}}{l o g 2^{4}} - \frac{l o g 5^{3}}{l o g 5^{2}} + \frac{l o g 3^{3}}{l o g 3^{2}}$

= $\frac{5 l o g 2}{4 l o g 2} - \frac{3 l o g 5}{2 l o g 5} + \frac{3 l o g 3}{2 l o g 3}$

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

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Evaluate $l o g_{16}^{32}$ - $l o g_{25}^{125}$ + $l o g_{9}^{27}$

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