/*! 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 11 Find logarithm. Give approximati... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 12: Problem 11

Find logarithm. Give approximations to four decimal places. \(\log 0.0326\)

Short Answer

Expert verified
\(\log_{10} 0.0326 \approx -1.4868\)

Step by step solution

01

Understand the Problem

The exercise asks to find the logarithm of 0.0326 to four decimal places. This problem involves using the logarithmic function, specifically the common logarithm (base 10).
02

Use a Calculator

Input the value 0.0326 into a scientific calculator and then use the 'log' function to get the logarithm of that value.
03

Write Down the Result

After computing, the result provided by the calculator should be the logarithm base 10 of 0.0326. Ensure that the answer is approximated to four decimal places.
04

Verify the Result

Double-check the result by re-entering the value into the calculator to ensure the value obtained is consistent. The value should be consistent with the logarithmic properties and known values.

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 Function
A logarithmic function is an inverse of an exponential function. It helps us find the exponent or power to which a base number must be raised to produce a given value. If you have an equation like 10\textasciicircum x = y, the equivalent logarithmic form would be \(\log_{10}(y) = x\). This means that x is the power you must raise 10 to get y. Logarithmic functions are essential for solving exponential equations easily. You will often see this function represented as \(\log_{b}(x)\), where b is the base we are using.
Base 10 Logarithm
The base 10 logarithm, or common logarithm, is frequently used and is denoted as \(\log(x)\). For example, \(\log(100) \) equals 2 because 10 raised to the power of 2 is 100. Here are some important points to remember about base 10 logarithms:
  • The common logarithm is often used in scientific calculations, as it is easy to compute with calculators.
  • It simplifies multiplication and division into addition and subtraction, respectively, through logarithmic properties.
  • It is handy in various fields such as engineering, science, and finance.
In the exercise, we used base 10 logarithm to find \(\log(0.0326)\), yielding a result of approximately -1.4863.
Logarithmic Properties
Understanding logarithmic properties helps to simplify complex calculations. Some key properties include:
  • \textbf{Product Property:} \(\log_b(MN) = \log_b(M) + \log_b(N)\)
  • \textbf{Quotient Property:} \(\log_b\left(\frac{M}{N}\right) = \log_b(M) - \log_b(N)\)
  • \textbf{Power Property:} \(\log_b(M^p) = p\log_b(M)\)
  • \textbf{Change of Base Formula:} \(\log_b(x) = \frac{\log_k(x)}{\log_k(b)}\), where k is any positive number
In the given example, properties such as the product or quotient property could break down more complicated logarithms into simpler parts. Reinforcing these properties will enhance your understanding and make you proficient in tackling logarithmic problems without always relying on technology.

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

Find each logarithm. Give approximations to four decimal places. \(\ln 388.1\)

Find each logarithm. Give approximations to four decimal places. \(\log \left(2.13 \times 10^{4}\right)\)

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

In the central Sierra Nevada of California, the percent of moisture that falls as snow rather than rain is approximated reasonably well by $$f(x)=86.3 \ln x-680$$ where \(x\) is the altitude in feet. (a) What percent of the moisture at 5000 ft falls as snow? (b) What percent at 7500 ft falls as snow?

If the function is one-to-one, find its inverse. \(g(x)=\sqrt{x+2}, \quad x \geq-2\)
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Mechanics Maths

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.