How can I solve more complex exponential equations?

[mathdad]

I can solve equations like 4^(x) = 16 or
5^(x + 1) = 25. However, there are exponential equations that a bit more involved. The following equation has two exponentials on the left side.

Solve for x.

5^(x - 2) + 8^(x) = 200

 

[MarkFL]

I can solve equations like 4^(x) = 16 or
5^(x + 1) = 25. However, there are exponential equations that a bit more involved. The following equation has two exponentials on the left side.

Solve for x.

5^(x - 2) + 8^(x) = 200

I don't believe you can solve that algebraically...I would use a numeric root-finding technique, such as the Newton-Raphson method, to approximate the solution to the desired number of decimal places:

$$x\approx2.5421632382360203811$$

 

[mathdad]

I don't believe you can solve that algebraically...I would use a numeric root-finding technique, such as the Newton-Raphson method, to approximate the solution to the desired number of decimal places:

$$x\approx2.5421632382360203811$$

Ok. Good to know. I don't feel so bad now.