SOLUTION: Solve: 5^x+3 = 6^x

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Question 63487: Solve:
5^x+3 = 6^x
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!

Solve:

5x+3 = 6x

Take the natural log of both sides:

ln(5x+3) = ln(6x)

Use the rule

ln(AN) = N·ln(A) on each side:

(x + 3)ln(5) = x·ln(6)

Let ln(5) = A and let ln(6) = B

(x + 3)A = xB

A(x + 3) = Bx

Ax + 3A = Bx

Ax - Bx = -3A

x(A - B) = -3A

Divide both sides by (A - B)

x = -3A/(A - B)

Now replace A by ln(5) and B by ln(6)

x = -3·ln(5)/( ln(5) - ln(6) )

Get calculator:

x = 26.38240736

Edwin