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How to compute this log?

 

\( \large \log_{x}{\frac{\sqrt{x}}{x}}=?\)

 Jun 30, 2020
 #1
avatar+21958 
+1

logx[ x1/2 / x ]  =  a     --->     x1/2 / x  =  xa 

 

Since x must be positive:  x1/2 / x  =  x-1/2  =  xa     --->     a  =  -1/2

                                                                                --->    logx[ x1/2 / x ]  =  -1/2 

 Jun 30, 2020
 #2
avatar+1154 
+1

so log means what power of the number under it is the number beside it and we get that sqrt(x) / (x)=sqrt[-2](x) and sqrt[-2](x)=x^-1/2 so logx sqrt(x) / (x) = x^-1/2

 Jun 30, 2020

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