# What is the vertical asymptote of a log function?

Logarithm functions are defined on

Thus, the

See general logarithms .

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The vertical asymptote of a log function is a vertical line that the graph of the function approaches but never touches or crosses. It occurs when the input of the logarithm approaches zero or becomes negative. For the common logarithm (base 10), the vertical asymptote is the line x = 0. For natural logarithm (base e), the vertical asymptote is the line x = 0 as well.

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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.

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.

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.

- How do you evaluate the limit #sin(x/5)/x# as x approaches #0#?
- How do you find the limit of #(x^2 - 8) / (8x-16)# as x approaches #2^+#?
- How do you find #lim 1/root3(x)# as #x->0^+#?
- How do you prove the statement lim as x approaches 6 for #((x/4)+3) = 9/2# using the epsilon and delta definition?
- How do you use the epsilon delta definition to prove that the limit of #x^3+6x^2=32# as #x->2#?

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