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) .............

member 587159

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