Question

Show that : log 300 = 3 log 2+2 log 3+log 5

Answer 1

sorry your R.H.S. is worng its right side is 2log2+2log3+log5 and its solution is. At the first the prime factor of 300=2×2×3×5×5
now taking. L.H.S.=log300
=log(2^2×3×5^2). where ^ is a power
we know that the log property log(m×n)=logm+long
therefore
=log2^2+log3+log5^2
again log property log m^n =nlogm

=2log2+log3+2log5. L.H.S. =R.H.S.

hence proved.