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How do you find the asymptotes for #ln(x-2)#?

Answer 1

Elijah Allen

#x=2#

The logarithm function (any base) is only defined for positive values, and and asymptote occurs for #x rarr 0#

Thus for ln(x-2) we have an asymptote as #x-2 rarr 0#, ie when #x=2#.

We can confirm this graphically:

graph{ln(x-2) [-5, 15, -15, 15]}

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Answer 2

Cora Alexander

To find the asymptotes of ( \ln(x-2) ), set the argument of the natural logarithm function, ( x-2 ), equal to zero and solve for ( x ). This gives the vertical asymptote. There are no horizontal asymptotes for the natural logarithm function.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.