Logarithm ProofDate: 6/18/96 at 13:58:42 From: Scott Turner Subject: Logarithm Proof I'm trying to show that a to the power of log base b of c is equal to c to the power of log base b of a. My textbook only has three theorems and I don't see how I can prove this from any of them. Thank you. Date: 6/18/96 at 16:4:43 From: Doctor Anthony Subject: Re: Discrete Math This result is immediate if you take logs base b of each side of the equation, using the rule that log(x^y) = ylog(x). We have a^(log(c)) = c^(log(a)) Here log means log to base b. Now take logs (base b) of both sides and we get: log(c)*log(a) = log(a)*log(c) which is true, so the original equation was true. Alternatively, start with this equation and go back to the first one I gave. -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
Search the Dr. Math Library: |
[Privacy Policy] [Terms of Use]
Ask Dr. Math^{TM}
© 1994-2013 The Math Forum
http://mathforum.org/dr.math/