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Chapter 3: Problem 40

Find each logarithm. Round to six decimal places. $$\ln 0.011$$

Short Answer

Expert verified
\(-4.509861\)

Step by step solution

01

Understanding the Natural Logarithm

The natural logarithm, denoted as \(\ln \), is the logarithm to the base e (Euler's number). The task is to find \(\ln 0.011\) and round the result to six decimal places.
02

Use a Calculator

To find \(\ln 0.011\), use a scientific calculator. Input the value 0.011 and then press the \(\ln\) button to compute the natural logarithm.
03

Record the Result

After calculating, the result from the calculator should be noted. Ensure the result is rounded to six decimal places.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Logarithm
A logarithm is a mathematical function that helps us understand how many times one number must be multiplied by itself to get another number. The natural logarithm, denoted by \(\text{ln}\), is a special type of logarithm that uses the base \(\text{e}\) (approximately 2.71828). In this exercise, we are interested in \(\text{ln}\ 0.011\). To find this, we will use a scientific calculator, as solving it by hand is complex and time-consuming.
Rounding
Rounding numbers is essential when working with logarithms, as it makes the results easier to understand and use. In this exercise, after we calculate \(\text{ln}\ 0.011\), we need to round the answer to six decimal places. For instance, if the calculator shows a result of -4.5098600061, we round it to -4.509860. This is done because the exercise specifies to round the answer to six decimal places, ensuring consistency and precision.
Scientific Calculator
To solve \(\text{ln}\ 0.011\), a scientific calculator is an indispensable tool. Here鈥檚 a quick guide on how to use it for this purpose:
  • Turn on the calculator
  • Enter the value 0.011
  • Press the \(\text{ln}\) button
  • Note down the result displayed on the screen
After doing this, you鈥檒l get a result that you should then round to six decimal places, as previously discussed. Using a scientific calculator ensures you get an accurate value for logarithms and other complex mathematical functions.

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Most popular questions from this chapter

Differentiate. $$f(t)=\ln \left[\left(t^{3}+3\right)\left(t^{2}-1\right)\right]$$

Differentiate. $$F(x)=\left(\log _{9} x\right)^{7}$$

Differentiate. $$f(x)=8^{x}$$

Differentiate. $$F(x)=7^{x} \cdot\left(\log _{4} x\right)^{9}$$

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