Is n a Variable or Fixed Constant in the Equation n^lnx = x?

  • Context: MHB 
  • Thread starter Thread starter tmt1
  • Start date Start date
Click For Summary
SUMMARY

The equation n^ln(x) = x establishes that n is a fixed constant rather than a variable. The identity a^{log_a(x)} = x holds true for suitable values of a, which are typically positive constants not equal to 1. In this context, n is specifically identified as e, the base of natural logarithms, confirming its status as a constant in the equation.

PREREQUISITES
  • Understanding of logarithmic identities
  • Familiarity with natural logarithms (ln)
  • Basic knowledge of exponential functions
  • Concept of fixed constants in mathematical equations
NEXT STEPS
  • Study logarithmic properties and identities
  • Explore the significance of the natural logarithm (ln) in calculus
  • Investigate the role of constants in mathematical equations
  • Learn about the applications of the number e in various mathematical contexts
USEFUL FOR

Mathematicians, students studying calculus, educators teaching logarithmic functions, and anyone interested in the properties of exponential equations.

tmt1
Messages
230
Reaction score
0
Hi,

I learned today that n^lx = x

Is this where n is a variable a a fixed constant?

Thanks ,

Tim
 
Mathematics news on Phys.org
The actual identity is:

$$a^{\log_a(x)}=x$$

For suitable values of $a$, usually taken to be a positive fixed value not equal to 1.
 
tmt said:
Hi,

I learned today that n^lx = x

Is this where n is a variable a a fixed constant?

Thanks ,

Tim

Hello.

But, yes, it is constant:

\log_e(x) \ \log_e(n)=\log_e(x) \rightarrow{}n=e

It is correct, isn't it?

Regards.
 

Similar threads

Undergrad Why fixed point iteration of ##x^3 = 1-x^2## doesn't converge when ##x_0= 0##
  • · Replies 16 ·
Replies
16
Views
1K
High School Popularizing a property for n-bonacci numbers without publishing it?
  • · Replies 12 ·
Replies
12
Views
2K
MHB Is this Trigonometric Expression a Constant Function of x?
  • · Replies 2 ·
Replies
2
Views
1K
MHB How Does Boyle's Law Explain the Pressure-Volume Relationship of CO2?
  • · Replies 3 ·
Replies
3
Views
4K
MHB Expression sin^n(x)/(sin^n(x)+cos^n(x))
  • · Replies 2 ·
Replies
2
Views
2K
High School What is the notation for denoting constants in a function?
  • · Replies 2 ·
Replies
2
Views
1K
MHB Solve Floor Equation 7: x^2=2x-1
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Converting this vector into polar form
  • · Replies 4 ·
Replies
4
Views
2K
MHB Positive Integer Solutions of $(x^2+y^2)^n=(xy)^{2014}$
  • · Replies 2 ·
Replies
2
Views
2K
MHB Coulomb's Constant in electron energy formula.
  • · Replies 1 ·
Replies
1
Views
1K