SOLUTION: what is the exact log of log 6 base 2 mulitplied by log 8 base six? I'm confused b/c they both have different bases so I cant just add the eight and six

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Question 674455: what is the exact log of log 6 base 2 mulitplied by log 8 base six? I'm confused b/c they both have different bases so I cant just add the eight and six
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

You need to convert so that the two logs are the same base. You can convert the base 2 log to base 6, or the base 6 log to base 2, or convert both to some other base -- in the end it won't matter because you will always get the same answer.

Conversion formula:

Let's convert the base 6 log to base 2.

Now let's do the original multiplication:

Which simplifies to:

But wait! There's more! Now what would you pay? Oh, sorry, this isn't a Ginzu Knives infomercial, is it...but there is more for all that.

Note that , so:

But, remember:

So

But then:

So

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it