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:
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log(9.49):
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log(8.19):
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log(-1.02):
A logarithm of a negative number is undefined in the real number system.
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log(5.33):
Let me know if you'd like further explanation or assistance.
Related Questions:
- What is the mathematical reason logarithms of negative numbers are undefined in the real number system?
- How do logarithms behave for numbers greater than 1 vs. numbers between 0 and 1?
- How can logarithmic calculations help in real-world applications like pH levels or decibels?
- What are the differences between natural logarithms and common logarithms?
- 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).
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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