# Solving Exponential Equations Algebraically

 Functions Exponential Functions Language English Language Precalculus Exponential and Logarithmic Functions

### Transcript

00:28

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

00:34

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

00:39

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

00:43

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

00:51

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

00:55

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

00:58

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

01:03

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

01:07

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

01:12

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]

01:20

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

01:25

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

01:30

that 2 exponent and distribute it through the original exponent which

01:34

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

01:40

plus 12 equals 5x subtract 4x from both sides

01:44

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