# Solving Exponential Functions

• February 20th 2008, 01:11 PM
onenameless
Solving Exponential Functions
I know several methods in finding the value o x, but i can't figure this one out:

5^(x+2) - 5^(x) = 24

So that says 5 to the power of x plus 2 minus 5 to the power of x equals 24.
• February 20th 2008, 01:33 PM
Soroban
Hello, onenameless!

Quote:

Solve for $x\!:\;\;5^{x+2} - 5^x \:= \:24$

We have: . $5^2\!\cdot\!5^x - 5^x \:=\:24$

Factor: . $(5^2-1)\!\cdot\!5^x\:=\:24\quad\Rightarrow\quad 24\cdot5^x\:=\:24 \quad\Rightarrow\quad 5^x \:=\:1$

Therefore: . $x \:=\:0$