# 3^x=12x-9

• November 10th 2011, 01:08 PM
physicsdreams
3^x=12x-9
How would one go about solving this algebraically?
I understand that I can graph it and find the points of intersection, in which case the answers are 1 and 3.

Can anyone provide a step by step solution to this problem algebraically?
• November 10th 2011, 01:18 PM
Plato
Re: 3^x=12x-9
Quote:

Originally Posted by physicsdreams
How would one go about solving this algebraically?
I understand that I can graph it and find the points of intersection, in which case the answers are 1 and 3. Can anyone provide a step by step solution to this problem algebraically?

One does not solve this type of equation using algebraically.
You need to understand the Lambert W Function.
• November 11th 2011, 03:59 PM
HallsofIvy
Re: 3^x=12x-9
"By inspection" $3^1= 3= 12(1)- 9$ so one solution is x= 1.
• November 11th 2011, 04:47 PM
Plato
Re: 3^x=12x-9
Quote:

Originally Posted by HallsofIvy
"By inspection" $3^1= 3= 12(1)- 9$ so one solution is x= 1.

One question: Does inspection qualify as an algebraic solution?
• November 17th 2011, 12:51 PM
HallsofIvy
Re: 3^x=12x-9
I would say it does! It does suffer from the weakness of not telling whether that is the only solution or not!