/*! 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 60 Find the following using a calcu... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 60

Find the following using a calculator. Round to four decimal places. $$\log 0.082$$

Short Answer

Expert verified
-1.0864

Step by step solution

01

Identify the logarithm to be calculated

The exercise requires finding the logarithm of 0.082, which can be represented as \(\text{log}(0.082)\).
02

Use a calculator

Enter 0.082 into the calculator and press the \(\text{log}\) button to find the value of the logarithm. Ensure the calculator is in the correct mode for base 10 logarithm calculation.
03

Note down the raw result from the calculator

The calculator should display a value. Write down this value, which should be around \(-1.08635983004\).
04

Round the result to four decimal places

Round the raw result to four decimal places. The value \(-1.08635983004\) rounds to \(-1.0864\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

logarithmic functions
A logarithm is a special kind of mathematical operation. It's the opposite of an exponentiation. When we talk about a logarithmic function, we're looking for the power that a certain base must be raised to, to get another number. For example, if we have \(2^3 = 8\), then \(\log_2 (8) = 3\). The function basically 'undoes' the exponential function.
In general, if \(b^y = x\), then \(\log_b (x) = y\). Here, \b\ is the base, \x\ is the result, and \y\ is the exponent (or power).
Keep in mind that logarithms only make sense if \x \ is positive and \b\ is a positive number not equal to 1.
base 10 logarithms
Base 10 logarithms are also known as common logarithms. They are usually written as \(\log(x)\) without any numerics to indicate the base. In base 10 log, we're trying to find out how many times 10 must be multiplied by itself to reach a given number. For example, \(\log (1000) = 3\) because \(10^3 = 1000\).
Calculators often have a base 10 logarithm button labeled as \(\log\). If you enter a number and press this button, you'll get the logarithm of that number to base 10. This is very useful for various calculations in science, engineering, and everyday life.
rounding numbers
When dealing with numerical results, it's often necessary to round the numbers for simplicity or better readability. Rounding means reducing the digits of a number while keeping its value close to the original.
We usually round to a specific number of decimal places. Here's how you do it:
  • Identify the digit at the place you are rounding to.
  • Look at the digit immediately after.
  • If this digit is 5 or higher, increase the rounding digit by 1.
  • If it's less than 5, keep the rounding digit as it is.
For example, rounding the number -1.08635983004 to four decimal places gives us -1.0864. This is because the fifth decimal place (5) is equal to 5, so we increment the fourth decimal place by 1.
Rounding helps in making numbers more manageable, avoiding extremely long decimals, and is used in many practical applications.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Use a graphing calculator to find the point \((s)\) of intersection of the graphs of each of the following pairs of equations. $$y=\left|1-3^{x}\right|, y=4+3^{-x^{2}}$$

Use a graphing calculator to find the approximate solutions of the equation. $$\log _{5}(x+7)-\log _{5}(2 x-3)=1$$

In Exercises \(77-80\) : a) Find the vertex. b) Find the axis of symmetry. c) Determine whether there is a maximum or a minimum value and find that value.[ 3.3] $$g(x)=x^{2}-6$$

Express as a single logarithm and, if possible, simplify. $$\log _{a}\left(x^{2}+x y+y^{2}\right)+\log _{a}(x-y)$$

Solve the logarithmic equation algebraically. Then check using a graphing calculator. $$\log (2 x+1)-\log (x-2)=1$$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.