2 log x+3logy-5log2 express in a single logarithm form
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Answer:
2log3+3log5+5log2
We know that, logx
y
=ylogx,
Using the above property we can reduce the given equation as,
=log3
2
+log5
3
+log2
5
=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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