Question

Prove that: 2log15/18 - log25/162 + log4/9 = log2

Answer 1

this is the answer for the given question.

hope my answer is helpful to you

Answer 2

Explanation


2 log 15/18 - log 25/162 + log 4/9
= 2 log 15 - 2 log 18 - log 25 + log 162 + log 4 - log 9
= 2 log 3*5 - 2 log 2*32 - log 52 + log 2*34 + log 22 - log 32
= 2 log 3 + 2 log 5 - 2 log 2 - 2 log 32 - log 52 + log 2 + log 34 + log 22 - log 32
= 2 log 3 + 2 log 5 - 2 log 2 - 2*2 log 3 - 2 log 5 + log 2 + 4 log 3 + 2 log 2 - 2 log 3
= 2 log 3 + 2 log 5 - 2 log 2 - 4 log 3 - 2 log 5 + log 2 + 4 log 3 + 2 log 2 - 2 log 3
= 2 log 3 - 2 log 3 + 4 log 3 - 4 log 3 +2 log 5 - 2 log 5 - 2 log 2 + log 2 + 2 log 2   //rearranging the like terms
= log 2  //cross out whichever cancel each other