Answer
$x=\ln(\ln 10)$ or $x\approx 0.834$
Work Step by Step
$e^{e^x}=10$ (Take the natural logarithm)
$\ln (e^{e^{x}})=\ln 10$ (Use the property $\ln (e^a)=a$)
$e^x=\ln 10$ (Take the natural logarithm)
$\ln ({e^{x}})=\ln (\ln 10)$ (Use the property $\ln (e^a)=a$)
$x=\ln(\ln 10)$
$x=0.834032....$
$x\approx 0.834$
Thus, $x=\ln(\ln 10)$ or $x\approx 0.834$.
