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##### Asked by: Rina Klappach

science space and astronomy# How do you find the asymptote of a logarithmic equation?

**Key Points**

- When graphed, the
**logarithmic function**is similar in shape to the square root**function**, but with a vertical**asymptote**as x approaches 0 from the right. - The point (1,0) is on the graph of all
**logarithmic**functions of the form y=logbx y = l o g b x , where b is a positive real number.

Thereof, how do you find the equation of the horizontal asymptote?

**To find horizontal asymptotes:**

- If the degree (the largest exponent) of the denominator is bigger than the degree of the numerator, the horizontal asymptote is the x-axis (y = 0).
- If the degree of the numerator is bigger than the denominator, there is no horizontal asymptote.

**properties**of exponents and

**logarithms**are very similar. With exponents, to multiply two numbers with the same base, you add the exponents. With

**logarithms**, the logarithm of a product is the sum of the

**logarithms**.

In respect to this, how do you find the asymptotes of an LN graph?

**Find** the vertical **asymptote** of the **graph** of f(x) = **ln**(2x + 8). Solution. Since f is a logarithmic function, its **graph** will have a vertical **asymptote** where its argument, 2x + 8, is equal to zero: 2x +8=0 2x = −8 x = −4 Thus, the **graph** will have a vertical **asymptote** at x = −4.

**Finding Horizontal Asymptotes of Rational Functions**

- If both polynomials are the same degree, divide the coefficients of the highest degree terms.
- If the polynomial in the numerator is a lower degree than the denominator, the x-axis (y = 0) is the horizontal asymptote.