Find x (8^x)^2 = (2^x)^2 + (4^x)^2
You asked:
Solve the equation \[{{8}^{x}}^{2} = {{2}^{x}}^{2} + {{4}^{x}}^{2}\] for the unknown \(x\).
MathBot Answer:
The solution is: \[x = \frac{\log{\left(\sqrt{\frac{1}{2} + \frac{\sqrt{5}}{2}} \right)}}{\log{\left(2 \right)}} \approx 0.34712096\]