Question

1/3log125/8-2log2/5+log80/125

Answer 1

Answer:

$3log2$

Step-by-step explanation:

Given

$\frac{1}{3} log( \frac{125}{8} ) - 2 log( \frac{2}{5} ) + log( \frac{80}{125} )$

Required

Solve

Apply logarithm rules

$log( \frac{125^{\frac{1}{3}}}{8^{\frac{1}{3}}} )- log( \frac{2^2}{5^2} ) + log( \frac{80}{125} )$

$log( \frac{5}{2}} )- log( \frac{4}{25} ) + log( \frac{80}{125} )$

Apply quotient rule

$log( \frac{5}{2} / \frac{4}{25} ) + log( \frac{80}{125} )$

$log( \frac{5}{2} * \frac{25}{4} ) + log( \frac{80}{125} )$

$log( \frac{100}{8} ) + log( \frac{80}{125} )$

Apply product rule

$log( \frac{100*80}{8*125} )$

$log( \frac{8000}{1000} )$

$log(8)$

Express 8 as 2^3

$log(2^3)$

$3log2$