Question

Prove...(log√27+log8+log√1000)÷log120=3/4

Answer 1

log root 27 + log 8 + log root 1000
= log(3× root 3 × 8 × 10 × root 10)
= log (240 × root 30)
= log ( 120 × 2 × root 30 )
= log ( 120 × root 4 × root 30 )
= log 120 + log root 120

(log 120 + log root 120)/log 120
= (log 120/ log 120) + (log root 120 / log 120)
= 1 + [1/2 × ( log 120/log120)
= 1 + 1/2
= 3/2
{ Pls check the question. It has to be 3/2 and not 3/4}