Use The Base-2 Log Table To Find Or Approximate The Value Of Each Logarithm.i. Log ⁡ 2 4 \log _2 4 Lo G 2 ​ 4 Ii. Log ⁡ 2 17 \log _2 17 Lo G 2 ​ 17 Iii. Log ⁡ 2 35 \log _2 35 Lo G 2 ​ 35 Provide Your Answers:i. $\log _2 4 = $ □ \square □ Ii. $\log _2 17 \approx $

Using the Base-2 Log Table to Find or Approximate Logarithm Values

In mathematics, logarithms are a fundamental concept used to solve various problems, particularly in algebra and calculus. A logarithm is the power to which a base number must be raised to produce a given value. In this article, we will explore how to use a base-2 log table to find or approximate the value of each logarithm. We will examine three specific logarithms: $\log _2 4$, $\log _2 17$, and $\log _2 35$.

Before we dive into the base-2 log table, let's briefly review the concept of logarithms. A logarithm is the inverse operation of exponentiation. In other words, if $a^b = c$, then $\log _a c = b$. For example, if we have $2^3 = 8$, then $\log _2 8 = 3$. This means that the logarithm of 8 with base 2 is 3, because 2 raised to the power of 3 equals 8.

A base-2 log table is a table that lists the logarithms of powers of 2. The table is typically organized in a way that the base-2 logarithm of each power of 2 is listed in the first column, and the corresponding power of 2 is listed in the second column. For example, the base-2 log table might look like this:

Finding the Value of Each Logarithm

Now that we have a base-2 log table, let's use it to find the value of each logarithm.

i. $\log _2 4$

To find the value of $\log _2 4$, we can refer to the base-2 log table. We see that the base-2 logarithm of 4 is 2, because 2 raised to the power of 2 equals 4. Therefore, $\log _2 4 = 2$.

ii. $\log _2 17$

To find the value of $\log _2 17$, we can refer to the base-2 log table. However, we don't see 17 in the table. This is because 17 is not a power of 2. To approximate the value of $\log _2 17$, we can use the fact that $\log _2 17$ is between the logarithms of the two powers of 2 that are closest to 17. In this case, the two powers of 2 are 16 and 32. We can use the base-2 log table to find the logarithms of these two powers of 2:

We see that the base-2 logarithm of 16 is 4, and the base-2 logarithm of 32 is 5. Therefore, $\log _2 17$ is approximately between 4 and 5. To be more precise, we can use the fact that $\log _2 17$ is approximately equal to the average of the logarithms of the two powers of 2 that are closest to 17. In this case, the average of 4 and 5 is 4.5. Therefore, $\log _2 17 \approx 4.5$.

iii. $\log _2 35$

To find the value of $\log _2 35$, we can refer to the base-2 log table. However, we don't see 35 in the table. This is because 35 is not a power of 2. To approximate the value of $\log _2 35$, we can use the fact that $\log _2 35$ is between the logarithms of the two powers of 2 that are closest to 35. In this case, the two powers of 2 are 32 and 64. We can use the base-2 log table to find the logarithms of these two powers of 2:

We see that the base-2 logarithm of 32 is 5, and the base-2 logarithm of 64 is 6. Therefore, $\log _2 35$ is approximately between 5 and 6. To be more precise, we can use the fact that $\log _2 35$ is approximately equal to the average of the logarithms of the two powers of 2 that are closest to 35. In this case, the average of 5 and 6 is 5.5. Therefore, $\log _2 35 \approx 5.5$.

In this article, we used a base-2 log table to find or approximate the value of each logarithm. We examined three specific logarithms: $\log _2 4$, $\log _2 17$, and $\log _2 35$. We found that $\log _2 4 = 2$, $\log _2 17 \approx 4.5$, and $\log _2 35 \approx 5.5$. We hope that this article has provided a clear understanding of how to use a base-2 log table to find or approximate logarithm values.
Q&A: Using the Base-2 Log Table to Find or Approximate Logarithm Values

In our previous article, we explored how to use a base-2 log table to find or approximate the value of each logarithm. We examined three specific logarithms: $\log _2 4$, $\log _2 17$, and $\log _2 35$. In this article, we will answer some frequently asked questions about using the base-2 log table to find or approximate logarithm values.

Q: What is a base-2 log table?

A: A base-2 log table is a table that lists the logarithms of powers of 2. The table is typically organized in a way that the base-2 logarithm of each power of 2 is listed in the first column, and the corresponding power of 2 is listed in the second column.

Q: How do I use a base-2 log table to find the value of a logarithm?

A: To use a base-2 log table to find the value of a logarithm, you need to refer to the table and find the logarithm of the power of 2 that is closest to the given value. If the given value is not a power of 2, you can use the fact that the logarithm is between the logarithms of the two powers of 2 that are closest to the given value.

Q: How do I approximate the value of a logarithm if it is not a power of 2?

A: To approximate the value of a logarithm if it is not a power of 2, you can use the fact that the logarithm is between the logarithms of the two powers of 2 that are closest to the given value. You can then use the average of the logarithms of these two powers of 2 to approximate the value of the logarithm.

Q: What are some common applications of logarithms?

A: Logarithms have many common applications in mathematics and science. Some examples include:

• Solving equations with exponents
• Finding the area under curves
• Calculating the probability of events
• Modeling population growth and decay
• Analyzing data in statistics and data science

Q: Can I use a base-2 log table to find the value of a logarithm with a different base?

A: No, a base-2 log table is only useful for finding the value of logarithms with base 2. If you need to find the value of a logarithm with a different base, you will need to use a different type of table or calculator.

Q: Are there any online resources that I can use to find the value of a logarithm?

A: Yes, there are many online resources that you can use to find the value of a logarithm. Some examples include:

• Online calculators that can perform logarithmic calculations
• Logarithmic tables and charts that you can download or print
• Online math libraries and databases that contain logarithmic functions and formulas

In this article, we answered some frequently asked questions about using the base-2 log table to find or approximate logarithm values. We hope that this article has provided a clear understanding of how to use a base-2 log table and has answered some of the most common questions about logarithms.

If you are interested in learning more about logarithms and how to use a base-2 log table, we recommend checking out the following resources:

• Online math libraries and databases that contain logarithmic functions and formulas
• Logarithmic tables and charts that you can download or print
• Online calculators that can perform logarithmic calculations
• Math textbooks and online courses that cover logarithmic functions and formulas

We hope that this article has been helpful in your understanding of logarithms and how to use a base-2 log table. If you have any further questions or need additional assistance, please don't hesitate to ask.