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Product Rule of Logarithms - Problem 2

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

Using the product rule for logarithms going the other direction. So what I mean by the other direction instead of going backwards putting them back to a single log. Sometimes here this is referred to us condensing.

So what we have is a log base 2 of 10 and we have another log base 2 of 7 plus x. And what we want to do is put this in together to be one log. Whenever we are adding, this is a sign that came from a multiplication so if you remember we have log base b of xy is equal to log base b of x plus log base b of y. And what we are doing this time is we are going from this step back to a single log. So what that means is we are basically just going to multiply the answer of these two logs together.

So doing that out we end up with log base 2 of 10 times 7 plus x. If you wanted to you could distribute your 10 through but you may not have to. Either way this is going to be the condensed form the single log of taking these two logarithms joining them together.

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