How Do I Solve This Natural Logarithm Problem?

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SUMMARY

The discussion focuses on solving the equation 1/3 = ln(x^2/(x-4)). Participants clarify that the natural logarithm (ln) is the inverse of the exponential function with base e. To solve for x, one should exponentiate both sides of the equation, leading to e^(1/3) = x^2/(x-4). This approach simplifies the problem and allows for further manipulation to isolate x.

PREREQUISITES
  • Understanding of natural logarithms (ln) and their properties
  • Knowledge of exponential functions, specifically base e
  • Algebraic manipulation skills for solving equations
  • Familiarity with inverse functions and their applications
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  • Learn how to manipulate logarithmic equations
  • Study the properties of exponential functions and their inverses
  • Practice solving equations involving natural logarithms
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Students studying calculus, mathematics enthusiasts, and anyone seeking to understand natural logarithms and their applications in solving equations.

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Homework Statement


This is my first time ever posting anything on here...but we just started working with ln? I know that it's the base e? or something like that...
but the problem is this...

1/3=ln(x^2/x-4)

Homework Equations


The Attempt at a Solution


I haven't attempted..i don't know how to do it o.o
 
Last edited:
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ln is the opposite of "e to the power of", just like how addition is the opposite of subtraction. That is, if you raise e to the power of a certain number, taking the ln of the result gives you back the original number.

I presume you have to solve for x in 1/3=ln(x^2/x-4). I'll get you started: what happens when you raise e to the power of both sides? That is, e^(1/3)=e^(ln(x^2/x-4)), which simplifies to...
 

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