(log6 36 +2log6 3)*log5 125

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First, simplify the expressions inside the parentheses using the properties of logarithms:

log6 36 = log6 (6^2) = 2
2log6 3 = log6 (3^2) = 2log6 3

So, the expression inside the parentheses simplifies to:

2 + 2log6 3 = 2 + 2log6 3 = 2(1 + log6 3)

Next, simplify the expression inside the parentheses further:

1 + log6 3 = log6 (6*3) = log6 18

So, the expression inside the parentheses simplifies to:

2*log6 18

Now, we can rewrite log6 18 in terms of log5:

log5 (18) = log5 (3*6) = log5 3 + log5 6

Now, we use the properties of logarithms to simplify the expression further:

log5 (3) = log5 (3)
log5 (6) = log5 (2*3) = log5 2 + log5 3

So, log5 18 can be written as:

log5 18 = log5 3 + log5 6 = log5 3 + (log5 2 + log5 3) = 2log5 3 + log5 2

Finally, substitute log5 18 back into our original expression:

2*(2log5 3 + log5 2) = 4log5 3 + 2log5 2

Therefore, the final simplified expression is:

4log5 3 + 2log5 2