Use A Logarithm Table To Evaluate The Following Expression:$\[ \frac{415.2 \times 0.0761}{135} \\]

Introduction

In mathematics, logarithm tables are used to simplify complex calculations by breaking down large numbers into smaller, more manageable parts. These tables are particularly useful when dealing with expressions that involve multiplication and division operations. In this article, we will explore how to use logarithm tables to evaluate the expression $\frac{415.2 \times 0.0761}{135}$.

Understanding Logarithm Tables

A logarithm table is a table that contains the logarithms of various numbers. The logarithm of a number is the power to which a base number (usually 10) must be raised to produce that number. For example, the logarithm of 100 is 2, because $10^2 = 100$. Logarithm tables are useful because they allow us to quickly look up the logarithm of a number, rather than having to calculate it from scratch.

Using Logarithm Tables to Evaluate Expressions

To use a logarithm table to evaluate an expression, we need to follow these steps:

1. Break down the expression: Break down the expression into smaller parts, such as multiplication and division operations.
2. Find the logarithm of each part: Use the logarithm table to find the logarithm of each part of the expression.
3. Add or subtract the logarithms: Add or subtract the logarithms of each part of the expression, depending on whether the operation is multiplication or division.
4. Find the antilogarithm: Use the antilogarithm table to find the antilogarithm of the result.

Evaluating the Expression

Let's apply these steps to the expression $\frac{415.2 \times 0.0761}{135}$.

Step 1: Break down the expression

The expression can be broken down into three parts: $415.2$, $0.0761$, and $135$.

Step 2: Find the logarithm of each part

Using the logarithm table, we find the logarithm of each part:

• $\log(415.2) = 2.6183$
• $\log(0.0761) = -1.1193$
• $\log(135) = 2.1309$

Step 3: Add or subtract the logarithms

Since the expression involves multiplication and division operations, we need to add the logarithms of the first two parts and subtract the logarithm of the third part:

• $\log(415.2 \times 0.0761) = 2.6183 - 1.1193 = 1.4990$
• $\log(415.2 \times 0.0761) - \log(135) = 1.4990 - 2.1309 = -0.6319$

Step 4: Find the antilogarithm

Using the antilogarithm table, we find the antilogarithm of the result:

• $\text{antilog}(-0.6319) = 0.5333$

Conclusion

In this article, we have shown how to use logarithm tables to evaluate the expression $\frac{415.2 \times 0.0761}{135}$. By breaking down the expression into smaller parts, finding the logarithm of each part, adding or subtracting the logarithms, and finding the antilogarithm, we were able to simplify the expression and find the result. This approach can be useful when dealing with complex calculations that involve multiplication and division operations.

Real-World Applications

Logarithm tables have many real-world applications, including:

• Finance: Logarithm tables are used to calculate interest rates and investment returns.
• Science: Logarithm tables are used to calculate the pH of a solution and the concentration of a substance.
• Engineering: Logarithm tables are used to calculate the stress and strain of materials.

Limitations

While logarithm tables are a useful tool for simplifying complex calculations, they have some limitations. For example:

• Accuracy: Logarithm tables can be inaccurate if the numbers are very large or very small.
• Speed: Logarithm tables can be slow to use if the numbers are complex or if the calculations are repeated many times.

Conclusion

Introduction

In our previous article, we explored how to use logarithm tables to evaluate expressions. In this article, we will answer some frequently asked questions about logarithm tables and provide additional information to help you understand this mathematical concept.

Q: What is a logarithm table?

A: A logarithm table is a table that contains the logarithms of various numbers. The logarithm of a number is the power to which a base number (usually 10) must be raised to produce that number.

Q: How do I use a logarithm table to evaluate an expression?

A: To use a logarithm table to evaluate an expression, you need to follow these steps:

1. Break down the expression: Break down the expression into smaller parts, such as multiplication and division operations.
2. Find the logarithm of each part: Use the logarithm table to find the logarithm of each part of the expression.
3. Add or subtract the logarithms: Add or subtract the logarithms of each part of the expression, depending on whether the operation is multiplication or division.
4. Find the antilogarithm: Use the antilogarithm table to find the antilogarithm of the result.

Q: What is the difference between a logarithm table and an antilogarithm table?

A: A logarithm table contains the logarithms of various numbers, while an antilogarithm table contains the antilogarithms of various numbers. The antilogarithm of a number is the number that has a certain logarithm.

Q: How do I choose the right logarithm table for my needs?

A: When choosing a logarithm table, consider the following factors:

• Base: Choose a table with a base that is relevant to your calculations. For example, if you are working with numbers that are typically expressed in base 10, choose a table with a base of 10.
• Range: Choose a table that covers the range of numbers you need to work with.
• Accuracy: Choose a table that is accurate to the level of precision you need.

Q: Can I use a logarithm table to evaluate expressions with negative numbers?

A: Yes, you can use a logarithm table to evaluate expressions with negative numbers. However, you need to be careful when working with negative numbers, as the logarithm of a negative number is not defined.

Q: Can I use a logarithm table to evaluate expressions with fractions?

A: Yes, you can use a logarithm table to evaluate expressions with fractions. However, you need to be careful when working with fractions, as the logarithm of a fraction is not defined.

Q: What are some common applications of logarithm tables?

A: Logarithm tables have many real-world applications, including:

• Finance: Logarithm tables are used to calculate interest rates and investment returns.
• Science: Logarithm tables are used to calculate the pH of a solution and the concentration of a substance.
• Engineering: Logarithm tables are used to calculate the stress and strain of materials.

Q: What are some limitations of logarithm tables?

A: While logarithm tables are a useful tool for simplifying complex calculations, they have some limitations. For example:

• Accuracy: Logarithm tables can be inaccurate if the numbers are very large or very small.
• Speed: Logarithm tables can be slow to use if the numbers are complex or if the calculations are repeated many times.

Conclusion

In conclusion, logarithm tables are a useful tool for simplifying complex calculations. By understanding how to use a logarithm table and choosing the right table for your needs, you can simplify expressions and find the result. While logarithm tables have some limitations, they are a valuable tool for anyone who needs to perform complex calculations.

Additional Resources

If you want to learn more about logarithm tables, here are some additional resources:

• Logarithm tables: You can find logarithm tables online or in books.
• Antilogarithm tables: You can find antilogarithm tables online or in books.
• Mathematical software: You can use mathematical software such as Mathematica or Maple to perform complex calculations.

Conclusion

In conclusion, logarithm tables are a useful tool for simplifying complex calculations. By understanding how to use a logarithm table and choosing the right table for your needs, you can simplify expressions and find the result. While logarithm tables have some limitations, they are a valuable tool for anyone who needs to perform complex calculations.