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Solving Exponential Equations with the 'Same' Base - Concept

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!

In the real world we often hear terms like exponential growth or exponential decay, when discussing solving exponential equations such as those used in compounding interest problems. In order to understand solving exponential equations, students should understand the significance of exponential functions and logarithmic functions.

Solving basic exponential functions. So here we have an exponential function that has 5 to a power equals 5 to a power. And the most important thing to notice is that if our bases are the same, our exponents have to be the same, okay? Or conversely if our exponents are the same, our bases have to be the same. So really all we know here is that 5 to something is equal to 5 to something, these somethings have to be the same. So I can just drop my fives and say, x+1 has to equal 4. Solve this as we would any other equation, which leave leave us with x=3, okay?
So just by knowing that if our bases are the same, our exponents have to be the same makes solving these problems really really easy.

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