SOLUTION: Evaluate the following expression : {{{ log(2,6) }}} × {{{ log(3,6) }}} - {{{ ( log (2,3) + log(3,2) ) }}}

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Evaluate the following expression : {{{ log(2,6) }}} × {{{ log(3,6) }}} - {{{ ( log (2,3) + log(3,2) ) }}}      Log On


   

Question 1035078: Evaluate the following expression :
+log%282%2C6%29+ × +log%283%2C6%29+ - +%28+log+%282%2C3%29++%2B++log%283%2C2%29+%29+
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
+log%282%2C6%29+ × +log%283%2C6%29+ - +%28+log+%282%2C3%29++%2B++log%283%2C2%29+%29++=+2.
To see this,
(log%282%2C2%29%2Blog%282%2C3%29) × (+log%283%2C3%29+%2Blog%283%2C2%29+) - ++log+%282%2C3%29 - log%283%2C2%29+
= (1%2Blog%282%2C3%29+) × (+1+%2Blog%283%2C2%29+) - ++log+%282%2C3%29- log%283%2C2%29+
= 1 + log%283%2C2%29 + log%282%2C3%29 + log%282%2C3%29%2Alog%283%2C2%29- ++log+%282%2C3%29- log%283%2C2%29+
= 1 + log%282%2C3%29%2Alog%283%2C2%29 = 1 + %28log3%2Flog2%29%2A%28log2%2Flog3%29 = 2 after using a change-of-base formula.