Question

2 log 5+ log 8 - 1/2 log 4

Answer 1

given in the question. :

$2 log(5) + log(8) - \frac{1}{2} log(4)$

to solve the given equation ,

Solution :

Formal to be used to solve the question ,

$a log(b) = log( {b}^{a} )$

$log(a) + log(b) = log(ab)$

$log(a) - log(b) = log( \frac{a}{b} )$

$log(10) = 1$

applying this formula in above question,

$log( {5}^{2} ) + log(8) - log( \sqrt{4} )$

$log(25) + log(8) - log(2)$

$log(25 \times 8) - log(2) = log(200) - log(2)$

$log( \frac{200}{2} ) = log(100 ) \\ log( {10}^{2} ) = 2 log(10) = 2$

Hence the answer is 2