# Exponential having ln exponent

1. Jul 1, 2016

### chwala

1. The problem statement, all variables and given/known data
How is $e^log√(1-x^2)$ equal to $√(1-x^2)?$

2. Relevant equations

3. The attempt at a solution

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

2. Jul 1, 2016

### Math_QED

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.

3. Jul 1, 2016

### SammyS

Staff Emeritus
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 , ...​

.

4. Jul 1, 2016

### Ray Vickson

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: Jul 1, 2016
5. Jul 2, 2016

### chwala

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