SOLUTION: solve the indicial equation -- 5^x = 3^(x+1)

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Question 164711: solve the indicial equation -- 5^x = 3^(x+1)
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
solve the indicial equation -- 

5%5Ex+=+3%5E%28x%2B1%29

Take the natural log of both sides:

ln%285%5Ex%29+=+ln%283%5E%28x%2B1%29%29

x%2Aln%285%29+=+%28x%2B1%29ln%283%29

To make solving easier,

let A+=+ln%285%29 and  B+=+ln%283%29

x%2AA+=+%28x%2B1%29B

Ax+=+B%28x%2B1%29

Ax+=+Bx%2BB

Ax-Bx=B

x%28A-B%29=B

x=B%2F%28A-B%29

Now replace A by ln%285%29 and B by ln%283%29

++x=ln%283%29%2F%28ln%285%29-ln%283%29%29+++ 

x=1.098612289%2F%281.609437912-1.098612289%29

x=1.098612289%2F%28.5108256238%29

x=2.150660103

Edwin