Question

Log{(a/b)/3}=1/2(log a + log b), then relation between a and b is

Answer 1

Good question. I also want to know the answer of this question.

Answer 2

log { ( a / b ) / 3 } = 1 / 2 ( log a + log b )

log { ( a / b ) × 1 / 3 } = 1 / 2 ( log a + log b )

log { a / ( b × 3 ) } = 1 / 2 { log a + log b )

log { a / 3b } = 1 / 2 log a + 1 / 2 log b

log { a / 3b } = log { a^( ½ ) } + log { b^( ½ ) }

log { a / 3b } = log √a + log √b

log { a / 3b } = log { √a × √b }

log { a / 3b } = log { √( ab ) }


Comparing both sides ,


a / 3b = √( ab )


Square on both sides ,


$= > ( \frac{a}{3b} ) {}^{2} = ( \sqrt{ab} ) {}^{2} \\ \\ \\ = > \frac{ {a}^{2} }{9 {b}^{2} } = ab \\ \\ \\ = > \frac{ {a}^{2} }{a} = 9 {b}^{2} \times b \\ \\ \\ = > a = 9 {b}^{3}$






Therefore, relation between a and b is : –

a = 9b³