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Trigonometry Examples
Step 1
Step 1.1
Set the argument of the logarithm equal to zero.
Step 1.2
Solve for .
Step 1.2.1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 1.2.2
Simplify .
Step 1.2.2.1
Rewrite as .
Step 1.2.2.2
Pull terms out from under the radical, assuming positive real numbers.
Step 1.2.2.3
Plus or minus is .
Step 1.3
The vertical asymptote occurs at .
Vertical Asymptote:
Vertical Asymptote:
Step 2
Step 2.1
Replace the variable with in the expression.
Step 2.2
Simplify the result.
Step 2.2.1
One to any power is one.
Step 2.2.2
Logarithm base of is .
Step 2.2.3
The final answer is .
Step 2.3
Convert to decimal.
Step 3
Step 3.1
Replace the variable with in the expression.
Step 3.2
Simplify the result.
Step 3.2.1
Use logarithm rules to move out of the exponent.
Step 3.2.2
Logarithm base of is .
Step 3.2.3
Multiply by .
Step 3.2.4
The final answer is .
Step 3.3
Convert to decimal.
Step 4
Step 4.1
Replace the variable with in the expression.
Step 4.2
Simplify the result.
Step 4.2.1
Raise to the power of .
Step 4.2.2
The final answer is .
Step 4.3
Convert to decimal.
Step 5
The log function can be graphed using the vertical asymptote at and the points .
Vertical Asymptote:
Step 6