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Quotient 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 quotient rule of logarithms to condense or put two logarithms back together. We know that the log of base b of x over y is the same thing as log base b of x minus log base b of y.

For this example what we’re actually doing is we’re going from the expanded subtraction version back to a single log. All you have to know is that the first one, log base b of x is going to go in the numerator. Going here that means our x is going to be in the numerator, log base 5 of x over the second one is going to be in the denominator, x plus 3.

Using the quotient rule of logarithms we we’re able to combine these two, condense then down into a single log.

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