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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
Set the numerator equal to zero.
Step 1.2.2
Solve the equation for .
Step 1.2.2.1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 1.2.2.2
Simplify .
Step 1.2.2.2.1
Rewrite as .
Step 1.2.2.2.2
Pull terms out from under the radical, assuming positive real numbers.
Step 1.2.2.2.3
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
Cancel the common factor of and .
Step 2.2.1.1
Factor out of .
Step 2.2.1.2
Cancel the common factors.
Step 2.2.1.2.1
Factor out of .
Step 2.2.1.2.2
Cancel the common factor.
Step 2.2.1.2.3
Rewrite the expression.
Step 2.2.2
Simplify the expression.
Step 2.2.2.1
Raise to the power of .
Step 2.2.2.2
Divide by .
Step 2.2.3
Logarithm base of is .
Step 2.2.4
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
Cancel the common factor of and .
Step 3.2.1.1
Factor out of .
Step 3.2.1.2
Cancel the common factors.
Step 3.2.1.2.1
Factor out of .
Step 3.2.1.2.2
Cancel the common factor.
Step 3.2.1.2.3
Rewrite the expression.
Step 3.2.2
One to any power is one.
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
Multiply by by adding the exponents.
Step 4.2.1.1
Multiply by .
Step 4.2.1.1.1
Raise to the power of .
Step 4.2.1.1.2
Use the power rule to combine exponents.
Step 4.2.1.2
Add and .
Step 4.2.2
Raise to the power of .
Step 4.2.3
Cancel the common factor of and .
Step 4.2.3.1
Factor out of .
Step 4.2.3.2
Cancel the common factors.
Step 4.2.3.2.1
Factor out of .
Step 4.2.3.2.2
Cancel the common factor.
Step 4.2.3.2.3
Rewrite the expression.
Step 4.2.4
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