2. Using decimal logarithms solve the given equation $\sqrt{x^{\log \sqrt{x}}}=10$.
2. First, we square the equation, and we get $x^{\log \sqrt{x}}=100$. Then we take the logarithm of $\log \sqrt{x}$. $\log x=\log 100$. We rearrange the equation, and we get $\frac{1}{2}(\log x)^{2}=2$. We find that $\log x= \pm 2$, and we get the solutions $x_{1}=100, x_{2}=\frac{1}{100}$.

![](https://cdn.mathpix.com/cropped/2024_06_07_59669f975316a35884bfg-11.jpg?height=63&width=1639&top_left_y=1156&top_left_x=206)

![](https://cdn.mathpix.com/cropped/2024_06_07_59669f975316a35884bfg-11.jpg?height=57&width=1639&top_left_y=1211&top_left_x=206)

![](https://cdn.mathpix.com/cropped/2024_06_07_59669f975316a35884bfg-11.jpg?height=60&width=1639&top_left_y=1261&top_left_x=206)

![](https://cdn.mathpix.com/cropped/2024_06_07_59669f975316a35884bfg-11.jpg?height=48&width=1636&top_left_y=1318&top_left_x=210)

![](https://cdn.mathpix.com/cropped/2024_06_07_59669f975316a35884bfg-11.jpg?height=63&width=1636&top_left_y=1365&top_left_x=207)