Does log(AB)=LogAxLogB?

Leah5467

Junior Member
Joined
Feb 28, 2019
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My question is Log(AB)=(LogA)(LogB)? Please help! Thank you!
 

Dr.Peterson

Elite Member
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Nov 12, 2017
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My question is Log(AB)=(LogA)(LogB)? Please help! Thank you!
If you were working on a test and needed to remember whether this is true, you could check with an example.

Using base ten logs, for example, you should know that \(\displaystyle \log(100) = 2\) and \(\displaystyle \log(1000) = 3\). (Why is that?)

Then, \(\displaystyle \log(100)\log(1000) = (2)(3) = 6\); but \(\displaystyle \log(100\cdot1000) = \log(100000) = 5\). These aren't equal; so your claim is false.

But you might see from this example that multiplying two powers of ten adds the exponents (that is, here, adds the numbers of zeros: \(\displaystyle 2 + 3 = 5\)); and that might remind you of the correct rule. Since the log is the exponent (that is, \(\displaystyle \log(10^n) = n\)), this means that the logs of the factors add: \(\displaystyle \log(AB) = \log(A) + \log(B)\).
 
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