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Check it outProduct Rule of Logarithms  Problem 1 5,252 views
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 of logarithms; so behind me I have a log where we are multiplying two things inside of the logarithms. 64 x is actually the same thing as 64 times x. So whenever we are multiplying inside the log we can break this up into addition of two logs.
The base remains the same, so what we end up with is log base 8 of one item so it's 64 for the first plus the log base 8 of the other item in this case x. So now using some properties of logs we can actually simplify one of this.
Log base 8 of 64 is saying what power of 8 will give us 64 which we know to be 2. So this whole term turns into 2 and we are left with the log base 8 of x on the outside. So using the product rule to write this as two different logarithms if we are going to hear this is using the term expand so you'll say expand this and you’d write it as two different logs.
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Concept (1)
Sample Problems (4)
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Product Rule of Logarithms
Problem 1 5,251 viewsSimplify:
log_{8}(64x) 
Product Rule of Logarithms
Problem 2 4,867 viewsSimplify:
log_{2}10 + log_{2}(7 + x) 
Product Rule of Logarithms
Problem 3 4,490 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 4 479 views
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