Algebra Examples

Graph y=2 log of x
Step 1
Find the asymptotes.
Tap for more steps...
Step 1.1
Set the argument of the logarithm equal to zero.
Step 1.2
Solve for .
Tap for more steps...
Step 1.2.1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 1.2.2
Simplify .
Tap for more steps...
Step 1.2.2.1
Rewrite as .
Step 1.2.2.2
Pull terms out from under the radical, assuming positive real numbers.
Step 1.2.2.3
Plus or minus is .
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
Logarithm base of is .
Step 2.2.2
Multiply by .
Step 2.2.3
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
Logarithm base of is .
Step 3.2.2
Multiply by .
Step 3.2.3
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
Simplify by moving inside the logarithm.
Step 4.2.2
Raise to the power of .
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