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Pre-Algebra Examples
Step 1
Step 1.1
Set the argument of the logarithm equal to zero.
Step 1.2
Solve for .
Step 1.2.1
Raise each side of the equation to the power of to eliminate the fractional exponent on the left side.
Step 1.2.2
Simplify the exponent.
Step 1.2.2.1
Simplify the left side.
Step 1.2.2.1.1
Simplify .
Step 1.2.2.1.1.1
Multiply the exponents in .
Step 1.2.2.1.1.1.1
Apply the power rule and multiply exponents, .
Step 1.2.2.1.1.1.2
Cancel the common factor of .
Step 1.2.2.1.1.1.2.1
Cancel the common factor.
Step 1.2.2.1.1.1.2.2
Rewrite the expression.
Step 1.2.2.1.1.2
Simplify.
Step 1.2.2.2
Simplify the right side.
Step 1.2.2.2.1
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
The natural logarithm of is .
Step 2.2.2
Multiply by .
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 by moving inside the logarithm.
Step 3.2.2
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 by moving inside the logarithm.
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