Math Problem Statement

Evaluate the following logarithms with a calculator. Round answers to four decimal places. If an expression doesn’t exist, write DNE as your answer: log(9.49), log(8.19), log(-1.02), log(5.33).

Solution

Here are the solutions to the logarithms, calculated to four decimal places:

  1. log(9.49):
    log(9.49)=0.9761\log(9.49) = 0.9761

  2. log(8.19):
    log(8.19)=0.9135\log(8.19) = 0.9135

  3. log(-1.02):
    A logarithm of a negative number is undefined in the real number system.
    Answer: DNE (Does Not Exist)\text{Answer: DNE (Does Not Exist)}

  4. log(5.33):
    log(5.33)=0.7261\log(5.33) = 0.7261

Let me know if you'd like further explanation or assistance.

Related Questions:

  1. What is the mathematical reason logarithms of negative numbers are undefined in the real number system?
  2. How do logarithms behave for numbers greater than 1 vs. numbers between 0 and 1?
  3. How can logarithmic calculations help in real-world applications like pH levels or decibels?
  4. What are the differences between natural logarithms and common logarithms?
  5. How can you use a calculator to approximate logarithms without a log button?

Tip:

Always check the base of the logarithm being used. If no base is specified, it is assumed to be 10 (common logarithm).

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Logarithms
Base 10 logarithms
Real number system

Formulas

log_b(x) = y implies b^y = x

Theorems

A logarithm of a negative number is undefined in the real number system.

Suitable Grade Level

Grades 9-12