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How do you find the domain and range of a natural log?

1 Answer
Feb 19, 2015

Hello,

The natural logarithm, also called neperian logarithm, is noted #ln#.

The domain is #D=]0,+\infty[# because #\ln(x)# exists if and only if #x>0#.

The range is #I=RR = ]-oo,+oo[# because #ln# is strictly croissant and #\lim_{x\to-oo} ln(x) = 0# and #\lim_{x\to+oo} ln(x) = +oo#.

graph{ln(x) [-2.125, 17.875, -4.76, 5.24]}

The domain #D# is the projection of the curve of #ln# on the x axe.

The range #I# is the projection of the curve on y axe.