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Product Rule of Logarithms  Problem 2
Carl Horowitz
Carl Horowitz
University of Michigan
Runs his own tutoring company
Carl taught upperlevel 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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Carl Horowitz
B.S. in Mathematics University of Michigan
He knows how to make difficult math concepts easy for everyone to understand. He speaks at a steady pace and his stepbystep explanations are easy to follow.
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Sample Problems (4)
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Product Rule of Logarithms
Problem 1 6,412 viewsSimplify:
log_{8}(64x) 
Product Rule of Logarithms
Problem 2 6,148 viewsSimplify:
log_{2}10 + log_{2}(7 + x) 
Product Rule of Logarithms
Problem 3 5,510 viewslog_{b}xy = log_{b}x + log_{b}y
Tip: let m = log_{b}x and n = log_{b}y 
Product Rule of Logarithms
Problem 4 1,434 views
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