Expert: David Hemmer - 4/7/2007

Question
I don't know how to write out the problem out on my key board so I'am going to write it out in english.
   
     5 to the (2x+1) power = 3 to the (4x-1) power

  Sorry about that.This is one simple exponential equation that that I don't know how to solve. In fact I don't know how to solve any of this type.I keep trying to take the ln of both sides while I subtract (2x+1) from the left side and divide ln 5 by ln 3.I know this is wrong but it seems like the only thing I can do.  

Answer
When you take ln of each side you will get:

(2x+1)ln5=(4x-1)ln3.

No just expand out and solve it like and an easy algebra problem, remember ln5 and ln3 are just numbers, not really different then 7 or 11! Gather the x terms on one side and the constant terms on the other.

2ln5*x + ln5= 4ln3*x -ln3

(2ln5-4ln3)*x=-ln5-ln3

x=(-ln5-ln3)/(2ln5-4ln3)