# With solution needed 2+log(a) (b)4-(a) (b)

1
by Nitya8

2015-04-05T17:55:16+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
2 + Log₃ 2 = X
X - 2 = Log₃ 2
3^(X - 2) = 2
(X - 2) Log₁₀ 3  = Log₁₀ 2
X = 2 + Log 2 / Log 3
=====================
Log₃  18 =  Log₃ 9*2  = Log₃ 3² + Log₃ 2
= 2 + Log₁₀ 2 / Log₁₀ 3
============================
Log₃ 25 = Log₃ 5² = 2 Log₃ 5  = 2 Log 5 / Log 3
===================
4 - Log₆ 2 = 4 - 1 / Log₂ 6
= 4 - 1 / [ Log₂ 2 + Log₂ 3 ]
= 4 - 1 / [ 1 + Log 3 / Log 2]
=  4 - Log 2 / (Log 2 + Log 3 ) = 4 - Log 2 / Log 6
=========================

log₆  648 = log₆  (3* 6 * 6* 6)
= Log₆ 6³ +Log₆ 3
= 3 + 1 / Log₃ 6
= 3 + 1 / [Log₃ 3 + Log₃ 2]
= 3 + 1 / [ 1 + Log 2 / Log 3 ]
= 3 + Log 3 / ( Log 3 + log 2 )      = 3 + Log 3 / Log 6
============================
Log₆ 125 =  Log₆ 5³ = 3 Log₆ 5 = 3 Log 5 / Log 6