Question

$x^{2logx}=10x^2$

Answer 1

The solutions are $x = 10^{\frac{1 + \sqrt{3}}{2}}$ and $x = 10^{\frac{1 - \sqrt{3}}{2}}$.

Answer 2

1. Take $\log_{10}$ on both sides of the equation.
2. Apply logarithm properties to transform the equation into a quadratic form in terms of $\log_{10}x$.
3. Solve the quadratic equation for $\log_{10}x$.
4. Convert the logarithmic solutions back to find the values of $x$.