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

Introduction to Logarithms

College Algebra

6. Exponential & Logarithmic Functions

Introduction to Logarithms

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0:49 minutes

Problem 81

Textbook Question

In Exercises 81–100, evaluate or simplify each expression without using a calculator. log 100

Verified step by step guidance

Recognize that the expression is a logarithm: \( \log 100 \).

Recall the definition of a logarithm: \( \log_b a = c \) means \( b^c = a \).

Identify the base of the logarithm. If no base is specified, it is assumed to be 10 (common logarithm).

Rewrite the expression using the definition: \( \log_{10} 100 = c \) means \( 10^c = 100 \).

Determine the value of \( c \) by finding the power to which 10 must be raised to equal 100.

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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, answering the question: to what exponent must a base be raised to produce a given number? For example, in the expression log_b(a), b is the base, and a is the number for which we want to find the exponent.

Common Logarithm

The common logarithm is a logarithm with base 10, often denoted as log(x) or log_10(x). It is widely used in mathematics and science, particularly for simplifying calculations involving powers of ten, such as log(100) = 2, since 10^2 = 100.

Properties of Logarithms

Logarithms have several key properties that simplify calculations, including the product, quotient, and power rules. For instance, log_b(m*n) = log_b(m) + log_b(n) and log_b(m/n) = log_b(m) - log_b(n). These properties are essential for evaluating and simplifying logarithmic expressions.