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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