SOLUTION: Solve 4^x + 6^x = 9^x I understand the math behind the answer to this problem, but what I’d like to know, is there a regimented way to approach this problem and similar ones? Or

Question 1150548: Solve 4^x + 6^x = 9^x
I understand the math behind the answer to this problem, but what I’d like to know, is there a regimented way to approach this problem and similar ones? Or is it just a hit and miss application of mathematical laws with the hope of hitting the right combination, or just being lucky? Is there a branch of mathematics that teaches methodical ways of solving math problems without relying on a eureka moment?
Thanks,
Ed
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Solve 4^x + 6^x = 9^x
I understand the math behind the answer to this problem, but what I’d like to know, is there a regimented way to approach this problem and similar ones? Or is it just a hit and miss application of mathematical laws with the hope of hitting the right combination, or just being lucky? Is there a branch of mathematics that teaches methodical ways of solving math problems without relying on a eureka moment?
Thanks,
Ed
===============
1st thing you notice is there's no integer solution for x.
The sum of 2 even numbers is not an odd number.
----------
Have to use iterative or graphical methods.
x =~ 1.18681439

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