(4^k)+(1/(4^k))=(257/16)
You asked:
Solve the equation \({4}^{k} + \frac{1}{{4}^{k}} = \frac{257}{16}\) for the variable \(k\).
MathBot Answer:
The 2 solutions to the equation are: \[\begin{aligned}k &= \frac{\log{\left(16 \right)}}{\log{\left(4 \right)}} \approx 2.0\\k &= - \frac{\log{\left(16 \right)}}{\log{\left(4 \right)}} \approx -2.0\end{aligned}\]