Question

plzz answer no 20 in the following image through logarithm

Answer 1

hope this wil help you...solved by my brother.

Answer 2

LHS = ( log√27 + log8 + log√1000 )/log120

= { log( 3√3) + log8 + log(10√10) }/log120

[ use , logm + logn = logmn ]

= { log( 3√3 × 8 × 10√10) }/log120

= { log( 240√30 )}/log120

= { log( 120 √120)}/ log120

[ use logmn = logm + logn ]

= { log120 + log√120}/log120

= log120/log120 + log(120)½/log120

[ use, log(x)ⁿ = nlogx ]

= 1 + 1/2 { log120/log120}

= 1 + 1/2 = 3/2 = RHS