# Exponential Theory: Explaining e^(-2 ln |x+1|) = e^ln [1/(x+1)^2]

• naspek
In summary: That's why I asked.In summary, the equation e ^ (-2 ln |x + 1|) is equivalent to e ^ ln [1 / (x + 1)^2] due to a known calculation rule for logarithms, which states that y alog(x) = alog(xy) for any number a. The more commonly used notation for this property is loga (xy) = y loga(x).
naspek
e ^ (-2 ln |x + 1|) = e ^ ln [1 / (x + 1)^2]

how can this happen?
can anyone explain to me the process of this equation..

Last edited:
Nice how you absolutely did not try to hide the fact that you copied this from another forum.

The answer to your question: it is a known calculation rule for logarithms that
y alog(x) = alog(xy)
for any number a.

CompuChip said:
Nice how you absolutely did not try to hide the fact that you copied this from another forum.

The answer to your question: it is a known calculation rule for logarithms that
y alog(x) = alog(xy)
for any number a.

I haven't see notation like that before. Is alog supposed to represent the log base a of something?

The notation that is used more often for this property of logarithms, I believe, is this:
loga (xy) = y loga(x)

Thanks Mark44 =)

Mark44 said:
I haven't see notation like that before. Is alog supposed to represent the log base a of something?

The notation that is used more often for this property of logarithms, I believe, is this:
loga (xy) = y loga(x)

Right, sorry.
Where I come from alog is standard notation.
But that is what I meant.

I figured that's what it meant, but it's something I haven't run across it before.

## 1. What is exponential theory?

Exponential theory is a mathematical concept that deals with exponential functions, which are functions that have a variable in the exponent. These types of functions are commonly used to model growth and decay.

## 2. What does e^(-2 ln |x+1|) = e^ln [1/(x+1)^2] represent?

This equation represents an exponential function with a negative exponent. The value of x+1 must be greater than 0 for the function to be defined.

## 3. How is exponential theory used in science?

Exponential theory is used in a variety of scientific fields, including biology, physics, and finance. It is commonly used to model population growth, radioactive decay, and compound interest.

## 4. What is the significance of ln (natural logarithm) in exponential theory?

The natural logarithm, ln, is the inverse of the exponential function. It is used to solve exponential equations and is also commonly used in calculus to find the rate of change of exponential functions.

## 5. How does e (Euler's number) relate to exponential theory?

Euler's number, e, is a mathematical constant that is the base of natural logarithms. It is used in exponential functions to determine the rate of growth or decay. It is also commonly used in various mathematical models and equations.

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