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Verified Answer :

f(x) = ln(x) 
f'(x) = 1/x 

f(1) = 0 
f'(1) = 1 

Now we know the slope of the line, let's search for the costant term: 
1x+a=f(x), for x=1: 

11+a=0 => a=-1 

linear approx: L(x) =1x-1. 

L(1.38) = 11.38-1 = 0.38 ~= ln(1.38)


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