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Solving Exponential Equations with the 'Same' Base - Problem 1

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!

Solving a exponential equation is pretty easy when our bases are the same because if our bases are the same, we know our exponents have to be the same. For this particular case, our bases are different though, we have 7 and 49 and what we really have to figure out is how we can make these bases the same.

So we need to think about is what do these two numbers have in common? They're both powers of 7, 49 we can rewrite as 7² so let's go ahead and do that. These sides are the same so I'm left with +1 and then this is just going to equal 7². Rewriting that 49 as a power of 7.

So what we've done is we've changed an equation with two different bases to now having the same base, so we know that x plus 1 has, oops I changed my plus to a minus, that looks like I did, that changes back to a minus. So I know that x minus 1 is equal to 2, solving this out x has equal 3, so even if we had different bases, take a second see if you can figure out what base they have in common, rewrite it and then solve.

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