How to Solve Equations with Unknown Exponents?

[foxyman20]

Ok i know this should be a relatively simple equation but i haven't done this stuff in so long i can't remember how to solve it. here goes.

4^(x+2) = 7^x +681

Solve for x

I know the answer is 3 from simple trial and error but i can't show the work to prove it and i know that harder problems exist so i would like to know the procedure. I'm pretty sure that either logs or natural logs (LN) is required somehow. Any help would be greatly appreciated.

Thanks.

 

[foxyman20]

well i figure the physics people should have no problem with this.

Ok i know this should be a relatively simple equation but i haven't done this stuff in so long i can't remember how to solve it. here goes.

4^(x+2) = 7^x +681

Solve for x

I know the answer is 3 from simple trial and error but i can't show the work to prove it and i know that harder problems exist so i would like to know the procedure. I'm pretty sure that either logs or natural logs (LN) is required somehow. Any help would be greatly appreciated.

Thanks.

 

[olgranpappy]

there's no easy way to solve an equation that has a polynomial on one side and a transcendental function on the other. Sorry.

P.S. there is another solution near 4.8622 too, but no other solutions besides that one.