How can I solve the equation (6^x+6^-x)/6 = 2?

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SUMMARY

The equation (6^x + 6^-x) / 6 = 2 can be solved by first multiplying both sides by 6^x, transforming it into a quadratic equation with the substitution y = 6^x. This results in the quadratic form y^2 - 12y + 6 = 0. Additionally, the hyperbolic cosine identity Cosh(t) = (e^t + e^-t) / 2 can be utilized for an alternative approach to solving the equation.

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I have the given equation: (6^x+6^-x)/6 = 2. How do you solve this?
 
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1. Multiply your equation with [tex]6^{x}[/tex]
2. You have now a quadratic equation in the unknown [tex]y=6^{x}[/tex]
As an alternative, use the identity:
[tex]Cosh(t)=\frac{e^{t}+e^{-t}}{2}[/tex]
 
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