Set the argument of the logarithm equal to zero.

Subtract from both sides of the equation.

The vertical asymptote occurs at .

Vertical Asymptote:

Vertical Asymptote:

Replace the variable with in the expression.

Simplify the result.

Add and .

Logarithm base of is .

The final answer is .

Convert to decimal.

Replace the variable with in the expression.

Simplify the result.

Add and .

Logarithm base of is .

The final answer is .

Convert to decimal.

Replace the variable with in the expression.

Simplify the result.

Add and .

Logarithm base of is .

Rewrite as an equation.

Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and does not equal , then is equivalent to .

Create expressions in the equation that all have equal bases.

Rewrite as .

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

Solve for .

The variable is equal to .

The final answer is .

Convert to decimal.

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

Vertical Asymptote:

Graph f(x) = log base 4 of x+3