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.
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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 .
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Replace the variable with in the expression.
Simplify the result.
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Simplify each term.
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Add and .
Logarithm base of is .
Multiply by .
Subtract from .
The final answer is .
Convert to decimal.
Find the point at .
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Replace the variable with in the expression.
Simplify the result.
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Simplify each term.
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Add and .
Logarithm base of is .
Multiply by .
Subtract from .
The final answer is .
Convert to decimal.
Find the point at .
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Replace the variable with in the expression.
Simplify the result.
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Simplify each term.
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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 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