Question

if 3(log5- log3) -(log5-2log6) = 2- logx, find x

Answer 1

Given, 3(log5 - log3) - ( log5 - 2log6 ) = 2 -logx

 We know that log a - log b = log a/b ---------- (1)

       3 log 5/3 - log 5/6^2 + logx = 2

       3 log 5/3 - log 5/36 + log x = 2

       We know that a log(x) = log(x)^a

       log (5/3)^3 - log 5/36 + log x = 2
  
       log 125/27 - log 5/36 + log x = log 100

      We know that log(a) - log(b) = log(a/b)

       log 125 * 36 /5 * 27 + log x = log 100

       log 100/3  + log x = log 100

      We  know that log(a + b) = log(ab)

       log 100x/3 = log 100

       x = 100 * 3/100

          = 3.

      x = 3.


Hope this helps!     

Answer 2

LHS: 3 log5 - 3 log3 - log 5 + 2 log6
= Log 5^3 * 6^2 /(3^3 * 5)
= log 100/3 = log 100 - log 3
= 2 - log 3.

Answer x = 3.