# Graph f(x)=2 log base 5 of x+3-1

Graph f(x)=2 log base 5 of x+3-1
Find the asymptotes.
Find where the expression is undefined.
Ignoring the logarithm, consider the rational function where is the degree of the numerator and is the degree of the denominator.
1. If , then the x-axis, , is the horizontal asymptote.
2. If , then the horizontal asymptote is the line .
3. If , then there is no horizontal asymptote (there is an oblique asymptote).
There are no horizontal asymptotes because is .
No Horizontal Asymptotes
No oblique asymptotes are present for logarithmic and trigonometric functions.
No Oblique Asymptotes
This is the set of all asymptotes.
Vertical Asymptotes:
No Horizontal Asymptotes
Vertical Asymptotes:
No Horizontal Asymptotes
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Add and .
Logarithm base of is .
Multiply by .
Subtract from .
The final answer is .
Convert to decimal.
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Add and .
Logarithm base of is .
Multiply by .
Subtract from .
The final answer is .
Convert to decimal.
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Add and .
Simplify by moving inside the logarithm.
Raise to the power of .
The final answer is .
Convert to decimal.
The log function can be graphed using the vertical asymptote at and the points .
Vertical Asymptote:
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### Name

Name six hundred ninety-five million ninety-three thousand one hundred eighty-six

### Interesting facts

• 695093186 has 16 divisors, whose sum is 1054736640
• The reverse of 695093186 is 681390596
• Previous prime number is 479

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 47
• Digital Root 2

### Name

Name one hundred two million seven hundred forty-eight thousand four hundred eighty

### Interesting facts

• 102748480 has 512 divisors, whose sum is 1409407776
• The reverse of 102748480 is 084847201
• Previous prime number is 587

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 34
• Digital Root 7

### Name

Name one billion nine hundred sixty-four million three hundred thirty-one thousand seven hundred sixty-nine

### Interesting facts

• 1964331769 has 4 divisors, whose sum is 1979326800
• The reverse of 1964331769 is 9671334691
• Previous prime number is 131

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 49
• Digital Root 4