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√log10x +log10√x = - ½
This equation can be written as (log10x)1/2+log10x1/2=-1/2
or
(log10x)1/2+1/2log10x=-1/2
Put (log10x)=t2
Now
t+t2/2=-1/2
(t+1)2=0
t=-1
(log10x)=1
x=101=10
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