Pre-Algebra Examples

Graph x^2 natural log of 3x
Step 1
Find the asymptotes.
Tap for more steps...
Step 1.1
Set the argument of the logarithm equal to zero.
Step 1.2
Divide each term in by and simplify.
Tap for more steps...
Step 1.2.1
Divide each term in by .
Step 1.2.2
Simplify the left side.
Tap for more steps...
Step 1.2.2.1
Cancel the common factor of .
Tap for more steps...
Step 1.2.2.1.1
Cancel the common factor.
Step 1.2.2.1.2
Divide by .
Step 1.2.3
Simplify the right side.
Tap for more steps...
Step 1.2.3.1
Divide by .
Step 1.3
The vertical asymptote occurs at .
Vertical Asymptote:
Vertical Asymptote:
Step 2
Find the point at .
Tap for more steps...
Step 2.1
Replace the variable with in the expression.
Step 2.2
Simplify the result.
Tap for more steps...
Step 2.2.1
One to any power is one.
Step 2.2.2
Multiply by .
Step 2.2.3
Multiply by .
Step 2.2.4
The final answer is .
Step 2.3
Convert to decimal.
Step 3
Find the point at .
Tap for more steps...
Step 3.1
Replace the variable with in the expression.
Step 3.2
Simplify the result.
Tap for more steps...
Step 3.2.1
Raise to the power of .
Step 3.2.2
Multiply by .
Step 3.2.3
Simplify by moving inside the logarithm.
Step 3.2.4
Raise to the power of .
Step 3.2.5
The final answer is .
Step 3.3
Convert to decimal.
Step 4
Find the point at .
Tap for more steps...
Step 4.1
Replace the variable with in the expression.
Step 4.2
Simplify the result.
Tap for more steps...
Step 4.2.1
Raise to the power of .
Step 4.2.2
Multiply by .
Step 4.2.3
Simplify by moving inside the logarithm.
Step 4.2.4
Raise to the power of .
Step 4.2.5
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