# Exponential having ln exponent

Gold Member

## Homework Statement

How is $e^log√(1-x^2)$ equal to $√(1-x^2)?$

## The Attempt at a Solution

taking ln on the function, ln√(1-x^2). lne⇒ ln√(1-x^2) .............

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Math_QED
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2019 Award

## Homework Statement

How is $e^log√(1-x^2)$ equal to $√(1-x^2)?$

## The Attempt at a Solution

taking ln on the function, ln√(1-x^2). lne⇒ ln√(1-x^2) .............
Log a = b <=> e^b = a.
Now notice on the right we have e^b = a, but we know b = log a. Therefor, e^log(a) = a. Apply this to your exercise.

SammyS
Staff Emeritus
Homework Helper
Gold Member

## Homework Statement

How is $e^{\log\sqrt{1-x^2}}$ equal to $\sqrt{1-x^2}?$

## The Attempt at a Solution

taking ln on the function, ln√(1-x^2). lne⇒ ln√(1-x^2) .............
Re: LaTeX.
To have more than a single character in a superscript or subscript or either part of a fraction or ... ,
place the desired string of characters inside a pair of braces: { ... } .

For many well-known functions, place a \ in front of the function name: e.g.: \ln , \sin , \tan , \sqrt , ...​

.

Ray Vickson
Homework Helper
Dearly Missed

## Homework Statement

How is $e^log√(1-x^2)$ equal to $√(1-x^2)?$

## The Attempt at a Solution

taking ln on the function, ln√(1-x^2). lne⇒ ln√(1-x^2) .............
It is good that you are trying to use LaTeX, but the next step is to learn to use it properly. Which of the following three expressions look best to you?
(1) $e^log√(1-x^2)$; (2) $e^{log√(1-x^2)}$; or (3) $e^{\log \sqrt{1-x^2}}$.
The first is a copy of what you wrote; the second inserts the brackets { and } needed with a multi-character exponent (or subscript); the third uses '\log' instead of 'log' and uses '\sqrt{ ...}' instead of '√' ; that also allows you to write and print 1-x^2 instead of (1-x^2), producing cleaner formula that is easier to read. You can right-click on each of the expressions to see their TeX structure.

Note added in edit: I see that SammyS has beaten me to it.

Last edited:
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Thanks a lot Ray Vickson and Sammy, next time i will type my work well in Latex. Noted.