SOLUTION: simplify:- (log3 135)/(log15 3)

SOLUTION: simplify:- (log3 135)/(log15 3) - (log3 5)/(log405 3)

Question 4212: simplify:-
(log3 135)/(log15 3) - (log3 5)/(log405 3)
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
first change the base, so that all are base 3...i will not write the base anymore, to ease the readability:

Since log3 to base 3 is 1, we get

135 = 5*27
405 = 5*81
and 15 = 5*3, so we get:

(log27+log5)(log3+log5) - log5(log81+log5)

log27log3 + log27log5 + log3log5 + (log5)^2 - log81log5 - (log5)^2

Now, log27 to base 3 is 3
and log81 to base 3 is 4, so...

3log3 + 3log5 + log5 + (log5)^2 - 4log5 - (log5)^2

everything cancels except for the 3, so this is the answer!

jon

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