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 two billion one hundred million six hundred forty-four thousand three hundred twenty-seven

Interesting facts

  • 2100644327 has 8 divisors, whose sum is 2159317776
  • The reverse of 2100644327 is 7234460012
  • Previous prime number is 1163

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 29
  • Digital Root 2

Name

Name one billion ten million seven hundred sixteen thousand five hundred four

Interesting facts

  • 1010716504 has 64 divisors, whose sum is 4127804064
  • The reverse of 1010716504 is 4056170101
  • Previous prime number is 17

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 25
  • Digital Root 7

Name

Name six hundred sixteen million eight hundred ninety-four thousand thirty-seven

Interesting facts

  • 616894037 has 4 divisors, whose sum is 627007116
  • The reverse of 616894037 is 730498616
  • Previous prime number is 61

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 44
  • Digital Root 8