# Problems of the form x^n*b^p(x)

• August 10th 2012, 04:50 PM
waldol1
Problems of the form x^n*b^p(x)
Okay, this is the equation: 25x=5x*x -3 * x. Solve for x.
• August 10th 2012, 04:55 PM
richard1234
Re: Problems of the form x^n*b^p(x)
I don't think that can be solved using algebraic methods. You have to approximate or use Newton's formula.
• August 10th 2012, 05:39 PM
Soroban
Re: Problems of the form x^n*b^p(x)
Hello, waldol1!

I assume you have a typo . . .

Quote:

$\text{Solve for }x\!:\;25^x \:=\:5^{x^2-3x}$

We have: . $(5^2)^x \:=\:5^{x^2-3x} \quad\Rightarrow\quad 5^{2x} \:=\:5^{x^2-3x}$

. . . . . . . . $2x \:=\:x^2-3x \quad\Rightarrow\quad x^2 - 5x \:=\:0 \quad\Rightarrow\quad x(x-5) \:=\:0$

Therefore: . $x \:=\:0,\:5$