SOLUTION: Hey, Quick question. I have the following problem: Using properties of logarithms, find the exact value of the expression: {{{ log(2, 25) log(3, 27) log(5, 8) }}} I kno

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Question 461820: Hey,
Quick question. I have the following problem:
Using properties of logarithms, find the exact value of the expression:

I know Change-of-Base formula, and that , but I don't know how to get to the answer, which is 18.
A little explanation of the steps would be much appreciated!
Thanks,
Jessica
Found 2 solutions by asuar010, solver91311:
Answer by asuar010(338) (Show Source):
You can put this solution on YOUR website!
the process is like a puzzle lol
first letts work with the simple one which is and the answer is 3 as you know because is 27...
then convert the rest of the equation and substitute and should look like this:
then using basic rules of multiplication of fraction rewrite as:
then go backwards on the second formula you wrote and the expression should be simplified as:
which becomes 2*3*3=18...
nice isn't?

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Ok, you are also going to need:

Also note that and

The trick is to change all three of your log functions to the same base, but it doesn't matter which base. I'm going to use natural logs, just because, well, it just seems natural.

Starting with

Do the base conversion to

Make the substitutions alluded to earlier:

Then use

Eliminating common factors leaves you with:

John

My calculator said it, I believe it, that settles it