Question

Prove log75/16 - 2log5/9 + log32/243

Answer 1

It is not given what to prove. but let us solve this to see where we reach

log (75/16) - 2 log (5/9) + log (32/243)

log 75 - log 16 - 2 (log 5 - log 9) + log 32 - log 243

log (3*5^2) - log (2^4) - 2log5 + 2 log3^2 + log 2^5 - log 3^5

log 3 + log 5^2 - log(2^4) - 2 log5 + 4log3 + log 2^5 - log 3^5

log3 + 2log5 - 4log2 -2log5 + 4log3 + 5log2 - 5log3

5log2 - 4log2 + log3 + 4log3 - 5log3 + 2log5 - 2log5

log2