Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

6. Exponential & Logarithmic Functions

Properties of Logarithms

College Algebra

6. Exponential & Logarithmic Functions

Properties of Logarithms

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1:43 minutes

Problem 43

Textbook Question

Solve each problem. Use a calculator to find an approximation for each logarithm. log 398.4

Verified step by step guidance

Understand that the problem requires finding the logarithm of 398.4, which is expressed as \( \log_{10}(398.4) \).

Recall that \( \log_{10}(x) \) represents the power to which the base 10 must be raised to obtain the number \( x \).

Use a calculator to find the approximate value of \( \log_{10}(398.4) \).

Enter 398.4 into the calculator and press the 'log' button to compute the logarithm.

The calculator will display the approximate value of \( \log_{10}(398.4) \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Logarithms

A logarithm is the inverse operation to exponentiation, representing the power to which a base must be raised to obtain a given number. For example, in the expression log_b(a) = c, b^c = a. Logarithms are essential for solving equations involving exponential growth or decay and are commonly used in various fields such as science and finance.

Common Logarithm

The common logarithm is a logarithm with base 10, denoted as log(x) or log_10(x). It is widely used in calculations involving large numbers, as it simplifies multiplication and division into addition and subtraction. Understanding how to use a calculator to compute common logarithms is crucial for solving problems that require approximating values.

Calculator Functions

Most scientific calculators have built-in functions for calculating logarithms, typically labeled as 'log' for common logarithms and 'ln' for natural logarithms (base e). Familiarity with these functions allows students to efficiently compute logarithmic values, which is essential for solving problems that involve logarithmic equations or approximations.