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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
Convert the decimal exponent to a fractional exponent.
Step 1.2.1.1
Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there is number to the right of the decimal point, place the decimal number over . Next, add the whole number to the left of the decimal.
Step 1.2.1.2
Reduce the fraction.
Step 1.2.1.2.1
Convert to an improper fraction.
Step 1.2.1.2.1.1
A mixed number is an addition of its whole and fractional parts.
Step 1.2.1.2.1.2
Add and .
Step 1.2.1.2.2
Cancel the common factor of and .
Step 1.2.1.2.2.1
Factor out of .
Step 1.2.1.2.2.2
Cancel the common factors.
Step 1.2.1.2.2.2.1
Factor out of .
Step 1.2.1.2.2.2.2
Cancel the common factor.
Step 1.2.1.2.2.2.3
Rewrite the expression.
Step 1.2.2
Raise each side of the equation to the power of to eliminate the fractional exponent on the left side.
Step 1.2.3
Simplify the exponent.
Step 1.2.3.1
Simplify the left side.
Step 1.2.3.1.1
Simplify .
Step 1.2.3.1.1.1
Multiply the exponents in .
Step 1.2.3.1.1.1.1
Apply the power rule and multiply exponents, .
Step 1.2.3.1.1.1.2
Cancel the common factor of .
Step 1.2.3.1.1.1.2.1
Factor out of .
Step 1.2.3.1.1.1.2.2
Cancel the common factor.
Step 1.2.3.1.1.1.2.3
Rewrite the expression.
Step 1.2.3.1.1.1.3
Divide by .
Step 1.2.3.1.1.2
Simplify.
Step 1.2.3.2
Simplify the right side.
Step 1.2.3.2.1
Simplify .
Step 1.2.3.2.1.1
Divide by .
Step 1.2.3.2.1.2
Raising to any positive power yields .
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 by moving inside the logarithm.
Step 2.2.2
The final answer is .
Step 3
The log function can be graphed using the vertical asymptote at and the points .
Vertical Asymptote:
Step 4