SOLUTION: how do you condense a problem like {{{ log3-log4-log7 }}}?

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Question 171046: how do you condense a problem like ?
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

The appropriate logarithm rules to apply are:

1. and

2.

First thing is to apply the Associative and Distributive Properties:

Now, using Rule 1., you can render the part in parentheses as:

and substitute, thus:

Now apply rule 2., thus:

Since is already reduced to lowest terms, you are done.

Check the reasonability of your answer with a calculator:

(roughly)

(roughly)

(roughly)

and

So far, so good. Since , the log of something smaller than 1, in particular must be less than zero.

Again, from the calculator: (roughly) and .

Close enough.