Questions on Algebra: Linear Algebra (NOT Linear Equations) answered by real tutors!

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Question 164711: solve the indicial equation -- 5^x = 3^(x+1): solve the indicial equation -- 5^x = 3^(x+1)
Answer by Edwin McCravy(2199) About Me  (Show Source):
You can put this solution on YOUR website!
solve the indicial equation -- 

5^x = 3^(x+1)

Take the natural log of both sides:

ln(5^x) = ln(3^(x+1))

x*ln(5) = (x+1)ln(3)

To make solving easier,

let A = ln(5) and  B = ln(3)

x*A = (x+1)B

Ax = B(x+1)

Ax = Bx+B

Ax-Bx=B

x(A-B)=B

x=B/(A-B)

Now replace A by ln(5) and B by ln(3)

  x=ln(3)/(ln(5)-ln(3))    

x=1.098612289/(1.609437912-1.098612289)

x=1.098612289/(.5108256238)

x=2.150660103

Edwin