How to solve this exponential equation ?

Question

(√10)/(0.1^x) = (1)/(10^5)

Answer 1

(√10) / (0.1)^x = 1 / 10⁵

(10^1/2) / (10^-1)^x = 10^-5          convert all to base 10

10^1/2 / 10^-x = 10^-5                power to power rule

10^1/2+x = 10^-5                      division of powers

1/2 + x = -5                          equal numbers on like bases have equal powers

x = -5.5                                subtract 1/2 from both sides