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Question

Write 2log3+3log5+5log2 as a single logarithm.

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Solution

2log3+3log5+5log2
We know that, logxy=ylogx,
Using the above property we can reduce the given equation as,
=log32+log53+log25
=log9+log125+log32
also, logx+logy+logz=logxyz, hence we can write the above as,
=log(9×125×32)
=log(36000)
2log3+3log5+5log2 can be written as a single logarithm as log36000.

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