/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 17 Use a calculator to find each of... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Use a calculator to find each of the following to four decimal places. $$\log 0.75$$

Short Answer

Expert verified
\(\log(0.75) = -0.1255\).

Step by step solution

01

Identify the Problem

The task is to find the logarithm of the number 0.75 to four decimal places.
02

Use the Logarithm Function on Calculator

Turn on the calculator and find the 'log' button (it stands for base 10 logarithm).
03

Input the Number 0.75

Press the 'log' button and then input the number 0.75 into the calculator.
04

Compute and Note the Result

After inputting the number, press the equals button ('='). The calculator should provide the value of \(\text{log}(0.75)\) to four decimal places.

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Key Concepts

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

Using a Calculator
Calculators are essential tools for solving problems involving logarithms. They help to quickly achieve precise results without manual computations. Here's a step-by-step guide:
1. **Turn on the Calculator**: Make sure your calculator is functional and powered up.
2. **Find the 'Log' Button**: Look for the 'log' button on your calculator. This button represents the common logarithm, which is the logarithm with base 10.
3. **Input the Number**: Enter the number for which you want to find the logarithm. In this case, enter 0.75.
4. **Compute the Logarithm**: Press the '=' button to compute the result. Your calculator should display the logarithmic value, which you should note down to the required decimal places.
Using a calculator simplifies the routine aspects of calculating logarithms, freeing you to focus on understanding and applying the results.
Logarithm Function
The logarithm function is crucial in mathematics and applies to various fields like science and engineering.
A logarithm answers the question: 'To what exponent must a base be raised, to produce a given number?' When we write \( \text{log}(x) \), it implies the base 10 logarithm, meaning \( 10^y = x \). For example, \( \text{log}(0.75) \) asks, 'To what power must 10 be raised to get 0.75?'
When we plug 0.75 into a calculator and press the 'log' button, the calculator performs this function for us, giving the exponent (or the logarithm) that makes the equation true.
This is particularly useful in fields requiring exponential scale comparison or data compression, as logarithms condense wide-ranging values into smaller, more manageable figures.
Decimal Places
Accuracy is vital in mathematical calculations, and specifying the number of decimal places ensures precision.
A 'decimal place' refers to the digits following the decimal point in a number. When you're asked to find \( \text{log}(0.75) \) to four decimal places, it means you need to provide the value accurate to four digits beyond the decimal.
This level of precision is often required in scientific contexts where even small differences can have significant impacts.
When using a calculator, you can achieve this by carefully reading the display and, if necessary, rounding the number to meet the required precision. For instance, if the calculator shows 0.751406, we'll round it to 0.7514 to meet the 'to four decimal places' requirement.
Understanding decimal places and how to manage them in your calculations ensures that your results remain accurate and reliable.

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