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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
Factor using the AC method.
Step 1.2.1.1
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Step 1.2.1.2
Write the factored form using these integers.
Step 1.2.2
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 1.2.3
Set equal to and solve for .
Step 1.2.3.1
Set equal to .
Step 1.2.3.2
Add to both sides of the equation.
Step 1.2.4
Set equal to and solve for .
Step 1.2.4.1
Set equal to .
Step 1.2.4.2
Subtract from both sides of the equation.
Step 1.2.5
The final solution is all the values that make true.
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
Simplify each term.
Step 2.2.1.1
Raise to the power of .
Step 2.2.1.2
Multiply by .
Step 2.2.2
Simplify by subtracting numbers.
Step 2.2.2.1
Subtract from .
Step 2.2.2.2
Subtract from .
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
Simplify each term.
Step 3.2.1.1
Raise to the power of .
Step 3.2.1.2
Multiply by .
Step 3.2.2
Simplify by subtracting numbers.
Step 3.2.2.1
Subtract from .
Step 3.2.2.2
Subtract from .
Step 3.2.3
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
Simplify each term.
Step 4.2.1.1
Raise to the power of .
Step 4.2.1.2
Multiply by .
Step 4.2.2
Simplify by subtracting numbers.
Step 4.2.2.1
Subtract from .
Step 4.2.2.2
Subtract from .
Step 4.2.3
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