MHB How can I solve more complex exponential equations?

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Complex exponential equations, such as 5^(x - 2) + 8^(x) = 200, often cannot be solved algebraically. Instead, numeric root-finding techniques like the Newton-Raphson method are recommended for finding approximate solutions. The approximate solution for the given equation is x ≈ 2.5421632382360203811. This approach helps in dealing with more intricate exponential equations effectively. Understanding these methods can alleviate frustration when facing challenging problems.
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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
 
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RTCNTC said:
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:

$$x\approx2.5421632382360203811$$
 
MarkFL said:
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.
 

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