6⋅( log_(4) x)^(2)+9⋅ log_(4) x=1
You asked:
Solve the equation \(6 \cdot {\log_{4}\left( x \right)}^{2} + 9 \cdot \log_{4}\left( x \right) = 1\) for the variable \(x\).
MathBot Answer:
The 2 solutions to the equation are: \[\begin{aligned}x &= 2^{- \frac{3}{2} + \frac{\sqrt{105}}{6}} \approx 1.1549458\\x &= 2^{- \frac{3}{2} - \frac{\sqrt{105}}{6}} \approx 0.10823019\end{aligned}\]