Finding N: Logarithmic Approach Needed

In summary, the conversation discusses finding the value of N for the equation {[pi^(N+1)] / (N+1)!} . {1/2^N} <= 10^-5, with the suggestion to try different integer values of N as the expression decreases with increasing N. The goal is to find the smallest N that satisfies the equation. Taking logs may be involved but it is not necessary to solve the problem.
  • #1
Fairy111
73
0

Homework Statement



I need to find N:

{[pi^(N+1)] / (N+1)!} . {1/2^N} <= 10^-5

Homework Equations





The Attempt at a Solution



I'm really struggling with this, i think taking logs is involved, but i can't seem to find a value of N.

Any help?
 
Physics news on Phys.org
  • #2
The expression decreases with increasing N. You basically want to evaluate it for various values of N until you figure out where it starts going below 10^(-5). You can only estimate log(n!) and the estimate doesn't lead to anything you can really solve.
 
  • #3
Do you need to find any N, or the smallest such N?
 
  • #4
I need to find what N needs to be bigger or equal to.
 
  • #5
Then just try some integer values for N. N doesn't have to be very big.
 

1. What is a logarithm?

A logarithm is the inverse function of exponential. It is used to solve for an unknown exponent in an exponential equation. In simple terms, a logarithm is the power to which a base number must be raised to get a specific number.

2. Why is a logarithmic approach needed in finding N?

A logarithmic approach is needed because it allows us to solve for N in complex exponential equations where N is the exponent. This is especially useful when dealing with large numbers or numbers with decimal places.

3. How does a logarithmic approach differ from other methods of solving for N?

Unlike other methods, a logarithmic approach uses the properties of logarithms to isolate and solve for N. This makes it more efficient and accurate, especially when dealing with large numbers.

4. Can logarithms be used in other fields besides mathematics?

Yes, logarithms have applications in various fields such as physics, chemistry, biology, and economics. They are used to model exponential growth and decay, measure sound levels, pH levels, and earthquake magnitudes, and calculate compound interest, among others.

5. Is there a specific formula for solving for N using logarithms?

Yes, there is a formula known as the logarithmic equation solver, which is used to solve for N. It involves taking the logarithm of both sides of an exponential equation and using the properties of logarithms to isolate N.

Similar threads

  • Calculus and Beyond Homework Help
Replies
7
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
492
  • Calculus and Beyond Homework Help
Replies
12
Views
815
  • Calculus and Beyond Homework Help
Replies
1
Views
253
  • Calculus and Beyond Homework Help
Replies
3
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
934
  • Calculus and Beyond Homework Help
Replies
1
Views
898
  • Calculus and Beyond Homework Help
Replies
3
Views
503
Replies
2
Views
828
  • Calculus and Beyond Homework Help
Replies
4
Views
604
Back
Top