What is \ln(e^x)?

Oberlaudacu

Oberlaudacu

Answered question

2021-12-30

What is ln(ex)?

Answer & Explanation

zesponderyd

zesponderyd

Beginner2021-12-31Added 41 answers

Explanation: 
You are seeking a number that is the exponent of ln  base, which provides us with the integrand, ex 
so: 
the base of ln  is e ; 
The exponent of this base must be this number in order to obtain ex is.....exactly x !!! 
so: 
ln(ex)=loge(ex)=x

Pansdorfp6

Pansdorfp6

Beginner2022-01-01Added 27 answers

Explanation:
ln(ex)=x because loga(ax) is x
Vasquez

Vasquez

Expert2022-01-08Added 669 answers

That's how simple it is, you need to remember this rule, thanks
nick1337

nick1337

Expert2023-05-11Added 777 answers

Answer: x
Explanation:
The expression ln(e^x) simplifies to x.
ln(ex)=x
Here, ln denotes the natural logarithm, e represents the base of the natural logarithm, and x is the variable.
madeleinejames20

madeleinejames20

Skilled2023-05-11Added 165 answers

To solve the expression ln(ex), we can follow these steps:
1. Recall the property of logarithms: ln(ab)=bln(a).
2. Apply the property mentioned above to the given expression: ln(ex)=xln(e).
3. Note that the natural logarithm base, e, is a special constant approximately equal to 2.71828. Therefore, ln(e)=1.
4. Substitute the value of ln(e) into the expression: ln(ex)=x·1.
5. Simplify the expression: ln(ex)=x.
Hence, the solution to ln(ex) is simply x.

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