Can k be equal to 4 in the equation k + 2 = 3^(n)?

  • Context: MHB 
  • Thread starter Thread starter mathdad
  • Start date Start date
Click For Summary
SUMMARY

The equation k + 2 = 3^(n) indicates that k must be an integer such that k + 2 results in a power of 3, where n is a positive integer. The discussion concludes that k cannot equal 4, as this results in k + 2 equaling 6, which is not a power of 3. Therefore, the only value of k that cannot satisfy the equation is 4.

PREREQUISITES
  • Understanding of exponential functions, specifically powers of 3.
  • Basic algebraic manipulation skills.
  • Knowledge of integer properties and positive integers.
  • Familiarity with mathematical reasoning and proof techniques.
NEXT STEPS
  • Study the properties of exponential functions, focusing on powers of integers.
  • Explore integer solutions to equations involving exponents.
  • Learn about modular arithmetic and its applications in number theory.
  • Investigate the characteristics of odd and even integers in mathematical equations.
USEFUL FOR

Students and educators in mathematics, particularly those focusing on algebra and number theory, as well as anyone interested in solving equations involving powers and integers.

mathdad
Messages
1,280
Reaction score
0
If n is a positive integer and k + 2 = 3^(n), which of the following could NOT be a value of k?

A. 1
B. 4
C. 7
D. 25
E. 79

I say the answer is B or 4.

When k = 4, k + 2 becomes 6.
However, there is no power we can raised 3 to that will yield 6.

Is my reasoning correct?
 
Mathematics news on Phys.org
RTCNTC said:
If n is a positive integer and k + 2 = 3^(n), which of the following could NOT be a value of k?

A. 1
B. 4
C. 7
D. 25
E. 79

I say the answer is B or 4.

When k = 4, k + 2 becomes 6.
However, there is no power we can raised 3 to that will yield 6.

Is my reasoning correct?
Looks good to me!

-Dan
 
Or since 3^(n) is odd, then k can't be 4.
 

Similar threads

Graduate Proving Goldbach's conjecture by induction (or why it doesn't seem to work)
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad Is this a proof of the Collatz Conjecture?
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Classify the isomorphism of a graph
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Number of Integers (<N) divisible only by one power of 2
  • · Replies 6 ·
Replies
6
Views
1K
Graduate Exploring Unconventional Addition: Can Mathematics Embrace New Foundations?
  • · Replies 8 ·
Replies
8
Views
2K
MHB Proving Divisibility by 6 Using Mathematical Induction
  • · Replies 7 ·
Replies
7
Views
3K
MHB Proving Inequality: \(\frac{1}{n^2}\) Sum < \(\frac{7}{4}\)
  • · Replies 2 ·
Replies
2
Views
1K
MHB Finding the Equation of a Circle Passing Through Three Given Points
  • · Replies 7 ·
Replies
7
Views
3K
MHB Recreational Number Theory, Unsolved Problem
  • · Replies 1 ·
Replies
1
Views
2K
MHB Powerful equation 5^m+7^n=k^3.
  • · Replies 7 ·
Replies
7
Views
2K