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Chapter 12: Problem 8

Find logarithm. Give approximations to four decimal places. \(\log 98\)

Short Answer

Expert verified
\(\log 98 \approx 1.9912\)

Step by step solution

01

Understand the Problem

The task is to find the value of \(\log 98\), which means finding the exponent to which 10 must be raised to obtain 98. The result should be approximated to four decimal places.
02

Use a Calculator

Enter the number 98 into the calculator and then press the \(\log\) button. This should give you the result.
03

Approximate to Four Decimal Places

The calculator should display roughly 1.991226. Round this number to four decimal places.
04

Write the Final Answer

After rounding, the logarithm of 98 to four decimal places is \(\log 98 \approx 1.9912\).

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Key Concepts

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

Logarithmic Calculations
Logarithms are used to determine the power to which a base number must be raised to get another number. In the exercise to find \( \log 98 \), we are essentially looking for the power to which 10 must be raised to yield 98. This type of logarithm, where the base is 10, is called a common logarithm.
Here is a step-by-step approach to solve the problem:
- First, understand that the logarithm function answers the question: 'To what exponent must 10 be raised, to get 98?'
- For solving, using a calculator simplifies the process significantly.
- Once you have the calculator's output, you can approximate this value to the desired number of decimal places.
Using a Calculator for Logarithms
Using a calculator to compute logarithms can make solving problems much faster and easier. Here's how you can do it step-by-step:
- Enter the number you want to find the logarithm for (in this case, 98) into the calculator.
- Then, press the \( \log \) button. This action will compute the common logarithm of the entered number.
- Your calculator should now display a numerical result which corresponds to \( \log 98 \).
This calculator-derived result gives you the exponent to which 10 must be raised to result in 98. Depending on your calculator model, the functions might be slightly different, but the principle remains the same.
Decimal Approximation
After using the calculator to find \( \log 98 \), you will need to express the result accurately. In many math problems, especially in higher education, it's crucial to approximate results to a specific number of decimal places.
In this exercise, the problem specifies rounding to four decimal places. The calculator gives a result like 1.991226. To approximate to four decimal places:
- Look at the fifth decimal place: In this case, 鈥�2鈥�.
- Since 鈥�2鈥� is less than 5, you don't round up; you keep the fourth decimal place as it is.
- Thus, \( \log 98 \approx 1.9912 \).
This final step ensures your result is precise and follows the problem's requirements.

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