If ` log_(a) 3 = 2 and log_(b) 8 = 3," then prove that "log_(a) b= log_(3) 4`.

If ` log_(a) 3 = 2 and log_(b) 8 = 3," then prove that "log_(a) b= log

1.	If ` log_(a) 3 = 2 and log_(b) 8 = 3," then prove that "log_(a) b= log_(3) 4`.
Answer» If ` log_(a) 3 = 2` ` rArr 3 = a^(2)` ` rArr a = sqrt3` If ` log_(b) 8 = 3` ` rArr 8 = b^(3)` ` rArr b = 2` So, ` log_(a) b = log_(sqrt3) 2 = x(let)` ` rArr 2 = (sqrt3)^(x)` ` rArr 4 = 3^(x)` ` rArr x = log_(3) 4`