2logy=0.5log16-log2+2log3

Question

This question is a topic in indices and logarithm.

Answer 1

Given :

2 log y = 0.5 log 16 - log 2 + 2 log 3.

Apply power property of logerthem :  log a ^n = n log a.

log y ^2 = log 16^0.5 - log 2 + log 3^2

Apply quotient property of logerthem : log (a/b) = log a - log b.

log y^2 = log ([16^0.5]/2) + log 3^2

Apply product property of logerthem : log (ab ) = log a + log b.

log y ^2 = log ([16^0.5]/2) * 3^2

            = log ([16^0.5]/2) * 9

Apply one - to - one property of logerthem : log a = log b ⇔ a = b.

y ^2 = ([16^0.5]/2) * 9

        = 4/2 * 9

        = 2 * 9

        = 18.

Extract square roots from each side.

y = sqrt (18)

   = 4.242.

The solution of y = 4.242.