CGTC FAQs: Academic Support

An exponential equation is an equation where the variable is an exponent.  In order to solve these equations you can either find a common base on both sides and set the exponents equal to one another. Another way you can solve these equations is to use logarithms to bring the variable down. These are often modeled to be used as compound interest and population growth. Now lets breakdown the two ways you can solve exponential functions.

1. You can solve by finding a common base 

Example: 2^x+5=2^2x+8

As you can see the bases are the same which is 2 so we can cross them out and drop our remainder

x+5=2x+8

Now we subtract x on both sides

x+8=5

Then we subtract 8 on both sides to get x by itself

So our solution is x=-3

2. You can solve by using logarithms 

The is the same as finding the common base but a bit different. In this case we isolate the exponential expression and then take the logarithm on both sides.

Here a couple examples

Lets say we have 3^x=81  we can rewrite this as log(3^x)=log(81)

use the logarithm property which is log(a^b)= b log(a) to bring the exponent down.

X log(3)= log(81)

Now we can solve for x.

X=log(81)/log(3) which it simplifies to x=4

2. 5^x=125 

log(5^x)=log(125)

Xlog(5)=log(125)

X=log(125)/log(5) which simplifies to x=3