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	= bx
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: