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4^2x-1=5^x+2

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2 Answers

 

4^(2x-1)=5^(x+2) <==Is this what you want?

Take ln,
(2x-1)ln4 = (x+2)ln5
Solve for x,
x = (2ln5+ln4)/(2ln4 - ln5) = 3.95922
This is a calculated answer:
 
x = 0.6318

Comments

Dear Galeboe:
 
When I interpreted the problem, I interpreted it as
 

(42x) - 1 = (5x) + 2

 
which, of course is quite different from the way Robert interpreted the question, to wit
 

4(2*x-1) = 5(x+2)

 
This is why learning to use parentheses and brackets is so important.  Chances are I was trying to solve the wrong system of equations.