# Solving exponential functions

• Jun 17th 2008, 11:46 AM
Arrazolo2007
Solving exponential functions
(-7x^2)(6^x)-10x6^x=0
• Jun 17th 2008, 11:59 AM
Moo
Hello !

Quote:

Originally Posted by Arrazolo2007
(-7x^2)(6^x)-10x6^x=0

$(-7x^2)({\color{red}6^x})-(10x)({\color{red}6^x})=0$

Factorising :

$0=({\color{red}6^x})(-7x^2-10x)$

A product of factors is equal to 0 if and only if one of its factors is equal to 0, that is to say that if you have $ab=0$, then $a=0$ or $b=0$. But $6^x \neq 0 \quad \text{for all x.}$

Therefore, $\dots=0$