Need help with simplifying this logarithm. \log_2 4^(2n) Would I just pull the 2n to the front: 2n∗log_2 4 So it would simplify to 4n Is this correct or am I completely wrong?

Edward Hendricks

Edward Hendricks

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2022-08-19

Simplifying/solving a logarithm log 2 4 2 n
Need help with simplifying this logarithm.
log 2 4 2 n
Would I just pull the 2n to the front:
2 n log 2 4
So it would simplify to
4 n
Is this correct or am I completely wrong?

Answer & Explanation

pelvogp

pelvogp

Beginner2022-08-20Added 18 answers

Remember that log a b = b log a. So log 2 4 2 n = 2 n log 2 4
And you know that log 2 4 = 2. If you ever get confused, just remember that log 10 1000 = 3 because 10 3 = 1000. So in this case, log 2 4 = 2 because 2 2 = 4
So you have 2 n log 2 4 = 2 n 2 = 4 n
Jazmin Clark

Jazmin Clark

Beginner2022-08-21Added 5 answers

log 2 4 2 n = log 2 2 2 2 n = log 2 2 4 n (since 4 = 2 2 ).
Now ask yourself the following question: to what power do I have to raise 2 to get 2 4 n ? That's 4 n, so log 2 4 2 n = 4 n
You are correct. :)

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