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### Logarithm Proof

```
Date: 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/
```
Associated Topics:
High School Logs

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