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chwala
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Homework Statement
How is ## e^log√(1-x^2)## equal to ##√(1-x^2)?##
Homework Equations
The Attempt at a Solution
taking ln on the function, ln√(1-x^2). lne⇒ ln√(1-x^2) ....
chwala said:Homework Statement
How is ## e^log√(1-x^2)## equal to ##√(1-x^2)?##Homework Equations
The Attempt at a Solution
taking ln on the function, ln√(1-x^2). lne⇒ ln√(1-x^2) ....
Re: LaTeX.chwala said:Homework Statement
How is ## e^{\log\sqrt{1-x^2}}## equal to ##\sqrt{1-x^2}?##Homework Equations
The Attempt at a Solution
taking ln on the function, ln√(1-x^2). lne⇒ ln√(1-x^2) ....
chwala said:Homework Statement
How is ## e^log√(1-x^2)## equal to ##√(1-x^2)?##Homework Equations
The Attempt at a Solution
taking ln on the function, ln√(1-x^2). lne⇒ ln√(1-x^2) ....
An exponential with a natural logarithm exponent is an expression of the form elnx where e is the base of the natural logarithm and x is the exponent. This type of exponential is commonly used in mathematics and science to model growth and decay.
To simplify an exponential with a natural logarithm exponent, you can use the property that elnx equals x. This means that the expression can be rewritten as just x, making the calculation much simpler.
The main difference between an exponential with a natural logarithm exponent and a regular exponential is the base. A regular exponential has a constant base, such as 2 or 10, while an exponential with a natural logarithm exponent has a variable base of e. This means that the growth or decay in an exponential with a natural logarithm exponent is continuous, while in a regular exponential it is discrete.
An exponential with a natural logarithm exponent can be used to model various real-life phenomena, such as population growth, radioactive decay, and compound interest. It is also used in many scientific equations and formulas to describe continuous processes.
Yes, an exponential with a natural logarithm exponent can have a negative value. This can occur when the exponent, x, is a negative number. In this case, the expression elnx would equal 1/e-x, which is a fraction with a negative exponent. However, the base, e, is always a positive number, so the overall value of the expression will be positive.