Find where the expression is undefined.

Since as from the left and as from the right, then is a vertical asymptote.

Ignoring the logarithm, consider the rational function where is the degree of the numerator and is the degree of the denominator.

1. If , then the x-axis, , is the horizontal asymptote.

2. If , then the horizontal asymptote is the line .

3. If , then there is no horizontal asymptote (there is an oblique asymptote).

There are no horizontal asymptotes because is .

No Horizontal Asymptotes

No oblique asymptotes are present for logarithmic and trigonometric functions.

No Oblique Asymptotes

This is the set of all asymptotes.

Vertical Asymptotes:

No Horizontal Asymptotes

Vertical Asymptotes:

No Horizontal Asymptotes

Replace the variable with in the expression.

Simplify the result.

Simplify each term.

Multiply by .

Logarithm base of is .

Add and .

The final answer is .

Convert to decimal.

Replace the variable with in the expression.

Simplify the result.

Multiply by .

The final answer is .

Convert to decimal.

Replace the variable with in the expression.

Simplify the result.

Multiply by .

The final answer is .

Convert to decimal.

The log function can be graphed using the vertical asymptote at and the points .

Vertical Asymptote:

Graph y = log of 2x+3