Problem 87 - Elementary and Intermediate Algebra

Question

Use a calculator to find each value. Give answers to four decimal places. See Using Your Calculator: Evaluating Logarithms. $$ \log 3.25 $$

Step-by-Step Solution

Answer

The value of \( \log 3.25 \) is approximately 0.5119.

Step 1: Access Calculator

Turn on your calculator and ensure it is in scientific mode to access logarithmic functions.

Step 2: Locate the Logarithm Function

Find the logarithm function on your calculator, often labeled as 'log'.

Step 3: Input the Number

Enter the number 3.25 into the calculator.

Step 4: Evaluate the Logarithm

Press the 'log' button or key to calculate the logarithm of the number you have entered.

Step 5: Record the Result

Read the output from the calculator screen, which shows the logarithm value to several decimal places. Ensure the output is rounded to four decimal places.

Step 6: Round to Four Decimal Places

Check the calculator's result and round the value to four decimal places. The number after the fourth decimal place will determine whether you round up or keep it the same.

Key Concepts

Calculator Usage

Using a calculator can significantly simplify complex mathematical tasks, especially when dealing with functions like logarithms. Whether you're solving logarithms or other mathematical expressions, the calculator can be your best friend.
Here are a few tips to get the most out of yours:

• Ensure the calculator is fully charged or has fresh batteries to avoid any interruptions during calculations.
• If using an online calculator, make sure your internet connection is stable.
• Familiarize yourself with the function layout. Functions like 'log' might be under a menu or need a shift key combination.
• Double-check your entries before calculating, and ensure you're in the right mode, such as scientific if evaluating anything beyond basic arithmetic.
• After obtaining your result, verify it by manually checking or using another calculator, if possible, especially for critical calculations.

Scientific Calculator

A scientific calculator is an essential tool for students and professionals involved in mathematics and science. This handy device can handle various functionalities, including calculating logarithms, trigonometric functions, and more.
These calculators often come with advanced features:

• Logarithmic Functions: Usually available as 'log' for base 10 and 'ln' for natural logarithms (base e).
• Multiple Modes: Scientific calculators can switch between different operational modes (e.g., degree, radian) depending on the function you are calculating.
• Memory Slots: Allows storing intermediate results to avoid re-calculating them during complex problems.
• Key Combinations: Often, multiple functions share keys, accessed using the shift or second function key. Understanding these can drastically improve efficiency.

The key strength of a scientific calculator lies in its versatility in handling both simple and complex calculations seamlessly.

Decimal Places

When you're working with logarithms or any mathematical computation that involves decimals, understanding decimal places is crucial. Decimal places represent the number of digits to the right of the decimal point.
Here's a quick guide on rounding decimal places effectively:

• Identify the required decimal place. For example, if you need four decimal places, find the fifth number.
• If the fifth number is 5 or more, round the fourth digit up. If it's less than 5, leave the fourth digit as it is.
• Check that your final result is logical and consistent with the expected range of the calculation for added accuracy.
• For scientific contexts, the precision offered by using more decimal places can be crucial, ensuring accuracy and reliability in results.

Understanding how to manage and interpret decimal places ensures that your calculations are both precise and practical, which is especially important in fields requiring high accuracy.