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

 Aug 12, 2019
 #1
avatar+8519 
+2

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

 

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

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

laugh  !
 

 Aug 12, 2019
edited by asinus  Aug 12, 2019
 #2
avatar+103122 
+2

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

 

 

cool cool cool

 Aug 12, 2019

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