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Graph of Logarithmic Functions - 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!

A recap of the graphs of logarithms, so we have basically two different graphs for logarithms. We have one where our base is going to be greater than one in which case our logarithmic graph is increasing. And one way that I remember that is we found this by dealing with a the inverse of a exponential graph with a base larger than one and this graph increases as well.

So a sort of one way you can remember is if your base is bigger than 1, your graph is going to be increasing it's going to be going up. The other side of that is dealing with a base between 0 and 1 we can never have negative bases so we have to go between 0 and 1.

And we got the logarithm graph from the exponential graph which is decreasing, getting smaller as does a logarithm graph. So whenever we are dealing with a base less than 1 and greater than 0, our graphs are going to decrease.

Those are the really the two main differences between our two log graphs. Other than that we know that they both have to pass through the point 1,0 because both of our exponential graphs pass through the point 0,1 inversely switched, our domain and range, domain has to be 0 to infinity not including 0, range can be everything and we have our vertical asymptote at x equals 0 for both.

So the rule and the main thing you have to remember is what your base is and what shapes are going this going to give you. I’m not going to do any examples but your basic transformations moving right and left moving up and down are going to hold true as well. So if we say plus 2 on the very outside you can move the graph up 2. All those things they are still going to hold. So just sort of a brief recap of all the graphs of logarithms all being 2.

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