To solve for x, we will take the logarithm of both sides of the equation.
10x10^x = 60
log(10x10^x) = log(60)
log(10) + log(10^x) = log(60)
1 + x log(10) = log(60)
x log(10) = log(60) - 1
x = (log(60) - 1) / log(10)
x ≈ 0.78
Rounding to the nearest hundredth, x ≈ 0.78.