Solving Exponential Equations
Example
If the graph of f(x) = b^{x} passes through
, find f(2).
Solution
First, we must find the base, b. Since the graph passes
through
we know that
when x
= 3.

y 
= b^{x} 
Replace y with
and x with
3.


= b^{ 3} 
Write
as . 

= b^{ 3} 
Rewrite


= b^{ 3} 
Since the exponents are the same, the
bases are equal. 

= b 
So, the base, b, of the exponential function is
. 
f(x) 

Now, we must find f(2). 


Substitute 2 for x.

f(2) 

Simplify. 


So,
.
Note:
Here's another way to find b:
