How to solve 8^x+13^x=108 algebraically

[beethoven'smahomeboy]

Help me solve for x in detail please:

8^x+13^x=108

Simply done graphically, but algebraically?

 

[Zurtex]

It can't be solved with logs or anything like that.

 

[beethoven'smahomeboy]

I figured as much after working with it for a while, but I thought I might have just been missing something. How does one solve it then?

 

[Zurtex]

You can only approximate the solution, which is:

$$x \approx 1.682790571570192534987737142973064792462$$

 

[dextercioby]

I think you can't do it,without a calculator.Maple returns $\left\{ x=1.\,68279\,0572\right\}$,but it can't be solved algebraically.In fact,most transcendental equations can't be solved.

Daniel.

 

[quentinchin]

you can solve it by using Newton-raphson method

 

[Curious3141]

you can solve it by using Newton-raphson method

Only approximate, not an exact solution. There is no exact solution method.