HELP PLEASE

What is the value of n  such that  \(10^n = 10^{-5}\times \sqrt{\frac{10^{73}}{0.001}} \)?

\(n\cdot log 10 = log (\)\(10^{-5}\times \sqrt{\frac{10^{73}}{0.001}}\))

\(n=log(10^{-5}\cdot \sqrt{\frac{10^{73}}{0.001}})\\ n=log(10^{-5}\cdot10^{38})\\ n=log (10^{33})\\ \color{blue}n=33\)

  !
 

10^n = 10^(-5) *  √ [ 10^73 / 0.001 ]

10^n  = 10^(-5) * ( 10^73 / 10 ^(-3) ) ^(1/2)

10^n =  10^(-5) * ( 10^76)^(1/2)  

10^n = 10^(-5) * 10^38

10^n = 10^33

n = 33