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Solving exponential equations algebraically a la shmoop

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Before we jump into solving exponential equations we'll [Person jumps into pool]

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probably make sure we know how to pick one out of a lineup an exponential

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function will usually be of the form f of x equals B to the X power or Cb to

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the X power where C is the coefficient if B, our base is

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greater than 1 and we're multiplying it by itself X number of times it's

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going to keep getting bigger in which case we have a growing function like our

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waistline if on the other hand it's smaller than 1 then multiplying it [formula appears on whiteboard]

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fights out they're just gonna keep shrinking resulting in it decaying function.....

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alright now that we know what these equations look like and what their [Man staring at exponential equation]

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exponents do to them we're ready to start solving so if we've got an

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exponential equation like 7 to the X power equals 7 to the y minus 3 power

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well then we can thank our lucky stars this ones a snap if the two sides [Shadow of hand clicks fingers]

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are equal and the bases are the same then the two exponents must be equal as

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well meaning that x equals the y -3 boom done if the bases are not the same but [Man and woman high five on a sofa]

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have a common denominator like this way then we can fiddle with them until they

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do have the same base in this case we can write 16 as 4 squared then just take

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that 2 exponent and distribute it through the original exponent which

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gives us 4 to the power of 4x plus 12 now both sides have 4 for a base so 4x

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plus 12 equals 5x subtract 4x from both sides

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and x equals 12 and that's pretty much the gist [Boy reading a book]

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