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Question

If log4=0.6020, then find the value of log80.


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Solution

Calculate the required logarithmic value

It is given that log4=0.6020.

As we know the common logarithm is treated as the logarithm with base 10.

So, the value of log80 can be calculated as,

log80=log1080

log80=log102×4×10 80=2×4×10

log80=log102+log104+log1010 [log(m×n)=logm+logn]

log80=12×2log102+log104+log1010

log80=12×log1022+log104+log1010 [nlogm=logmn]

log80=12×log104+log104+log1010

log80=12×0.6020+0.6020+log1010 log4=0.6020

log80=0.3010+0.6020+1 [log1010=1]

log80=1.9030

Hence, the required value of log80 is 1.9030.


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