1. ## 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?

2. ## Re: 3^x=12x-9

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.

3. ## Re: 3^x=12x-9

"By inspection" $\displaystyle 3^1= 3= 12(1)- 9$ so one solution is x= 1.

4. ## Re: 3^x=12x-9

Originally Posted by HallsofIvy
"By inspection" $\displaystyle 3^1= 3= 12(1)- 9$ so one solution is x= 1.
One question: Does inspection qualify as an algebraic solution?

5. ## 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!