# 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.
Logarithm base of is .
Multiply by .
Subtract from .
Convert to decimal.
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Logarithm base of is .
Multiply by .
Subtract from .
Convert to decimal.
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Simplify by moving inside the logarithm.
Raise to the power of .
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 eight hundred four million twenty-one thousand two hundred eighty-seven

### Interesting facts

• 804021287 has 4 divisors, whose sum is 804312360
• The reverse of 804021287 is 782120408
• Previous prime number is 2789

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 32
• Digital Root 5

### Name

Name one billion eight hundred three million one hundred eighty-two thousand five hundred fifty-seven

### Interesting facts

• 1803182557 has 4 divisors, whose sum is 1967108256
• The reverse of 1803182557 is 7552813081
• Previous prime number is 11

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 40
• Digital Root 4

### Name

Name four hundred fifteen million seven hundred nine thousand three hundred sixty-four

### Interesting facts

• 415709364 has 16 divisors, whose sum is 937969308
• The reverse of 415709364 is 463907514
• Previous prime number is 357

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 39
• Digital Root 3