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.
Hello, onenameless!
Solve for $\displaystyle x\!:\;\;5^{x+2} - 5^x \:= \:24$
We have: .$\displaystyle 5^2\!\cdot\!5^x - 5^x \:=\:24$
Factor: .$\displaystyle (5^2-1)\!\cdot\!5^x\:=\:24\quad\Rightarrow\quad 24\cdot5^x\:=\:24 \quad\Rightarrow\quad 5^x \:=\:1$
Therefore: .$\displaystyle x \:=\:0$