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Find log_x: \(x=\frac{\sqrt{10 \sqrt{10a}}}{0.1}\)

Guest Feb 4, 2018
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√[ 10 √(10a )]   =    10^(1/2) * (10a)^(1/4)  =  10^(1/2 + 1/4) * a*(1/4)  =

 

10^(3/4) * a^(1/4)

 

 

So  we have

 

10^(3/4) * a^(1/4)  / 0.1   =

 

10^(3/4) * a^(1/4)  /  (1/10)  =

 

10 * 10^(3/4) * a^(1/4)  =

 

10^(7/ 4) * a^(1/4)

 

So

 

log  [10^(7/ 4) * a^(1/4) ]   =

 

log [ 10^(7/4) ]  +  log a ^(1/4)  =

 

(7/4) log 10   +  (1/4) log a   =

 

(7/4)   +  log a  / 4  =

 

[ 7 + log a  ]  /  4

 

 

cool cool cool

CPhill  Feb 5, 2018

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