SOLUTION: I am stuck on the following problem: {{{2^x = 3^(x-1)}}} Thank you very much for providing me with your assistance.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: I am stuck on the following problem: {{{2^x = 3^(x-1)}}} Thank you very much for providing me with your assistance.       Log On


   

Question 17039: I am stuck on the following problem:
2%5Ex+=+3%5E%28x-1%29
Thank you very much for providing me with your assistance.

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Try this.
2%5Ex+=+3%5E%28x-1%29 Take the log of both sides.
xlog2+=+%28x-1%29log3Expand the right side.
xlog2+=+xlog3+-+log3 Subtract xlog3 from both sides.
xlog2+-+xlog3+=+-log3 Factor an x on the left side.
x%28log2+-+log3%29+=+-log3 Divide both sides by (log2 - log3)
x+=+%28-log3%29%2F%28log2+-+log3%29 You could just work it out on your calculator.
x+=+2.71