Question

Log(75/16)-2log5/9+log(32/243)=log 2

Answer 1

As Log ( A / B ) = Log A - Log B
Log (A)^ B = B Log A
Log ( AB ) = Log A + Log B

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

=> Log 75 - Log 16 - 2 ( Log 5 - Log 9 ) + Log 32 - Log 243

=> Log (5² * 3) - Log ( 2⁴) - 2 Log 5 + 2 Log 3² + Log 2⁵ - Log 3⁵

=> 2 Log 5 + Log 3 - 4 Log 2 - 2 Log 5 + 4 Log 3 + 5 Log 2 - 5 Log 3

=> (2 Log 5 - 2 Log 5) + ( Log 3 + 4 Log 3 - 5 Log 3 ) + (- 4 Log2 + 5 Log 2 )

=> Log 2

Hence Proved