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2logy=0.5log16-log2+2log3

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This question is a topic in indices and logarithm.

asked Feb 18, 2014 in ALGEBRA 1 by mathgirl Apprentice

1 Answer

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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 ba = 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.

 

answered Mar 28, 2014 by lilly Expert

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