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Introduction to Logarithms - Problem 1

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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!

Taking equations from exponential form and putting them into logarithm form. Now one of the most important things to remember is that your base of your exponential becomes the base of your log. So I have two different examples up here, they're pretty much exactly the same, the order is the different, so one has the exponent on one side the other one has it on the other, it doesn't really matter, we're just going to change put these into logarithmic form.

So we know we need a log and then there's three things that get filled in, there's the base, there's the thing with the log and there's the thing on the other side. The base remember stays the same, so the 5 is the base in this case, that means it's going to remain the base for our logarithm. The base always switches sides, so that would be coming over to the other side, so we end up with 25 and then the 2 stays where it is.

In general I have a harder time dealing with exponential to log, so it's always good for me to double check that I did it right whenever I did put it from log to exponential, the exponent comes up, bumps the term up, so this will become 5² equals 25 which is what I have right here.

Pretty much the exact same problem but instead of dealing with the exponent on the right we're now doing on left, we could switch the order because order doesn't matter at all. So we now want again log of a number, the base stays the same, that's 3, and remember the base is what switches sides, so the 1 over 81 doesn't change sides and that leaves us with the -4, the power by itself.

Again double checking if we put this from log to exponential, this 3 would come up and around bumping the -4 up you would end up with 1 over 81 is equal to 3 to the fourth. So taking a equation from exponential to log form. Making sure your base stays the base and everything else stays on the same sides.

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