Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Evaluate the expression:

[tex]\ln e^{-9} = \]


Sagot :

To solve the expression [tex]\(\ln e^{-9}\)[/tex], we can use properties of logarithms and exponents. Here's a step-by-step solution:

1. Understanding the notation: [tex]\(\ln\)[/tex] refers to the natural logarithm, which is the logarithm to the base [tex]\(e\)[/tex], where [tex]\(e\)[/tex] is approximately 2.71828.

2. Applying the logarithm property: One of the fundamental properties of logarithms is that [tex]\(\ln(e^x) = x\)[/tex]. This property is true because the natural logarithm function and the exponential function are inverses of each other.

3. Using the property on the given expression:
[tex]\[ \ln(e^{-9}) \][/tex]
According to the logarithmic property mentioned above, if we have [tex]\(\ln(e^x)\)[/tex], we can simplify it directly to [tex]\(x\)[/tex].

4. Simplifying the expression:
[tex]\[ \ln(e^{-9}) = -9 \][/tex]

Therefore, the value of [tex]\(\ln e^{-9}\)[/tex] is [tex]\(-9\)[/tex].
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.