How do you evaluate log3^4?

1 Answer
reudhreghs
Apr 30, 2016

1.908

Explanation:

A log tells you how many times you multiply the base by itself to get 3^4, or whatever else you put inside it. The base here isn't made explicit, so I'm going to assume it's 10, so

log_10 3^4

According to the law of logarithms where loga^n=nloga,

log_10 3^4=4log_10 3,

you can now simply use a calculator to find

4log_10 3approx4(0.477)=1.908

You can check this by doing

10^1.908=80.9approx81=3^4

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