What is the Basic Concept of Logarithms in Calculus?

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SUMMARY

The discussion centers on the application of logarithmic properties in calculus, specifically focusing on the expression log3(9 * (9)1/5). The user simplifies the expression to 96/5 and applies logarithmic rules to solve it. The key takeaway is the importance of understanding the properties of logarithms, such as the product and power rules, to manipulate and simplify logarithmic expressions effectively.

PREREQUISITES
  • Understanding of basic logarithmic properties, including product and power rules.
  • Familiarity with exponential expressions and their simplifications.
  • Basic knowledge of calculus concepts related to logarithms.
  • Ability to perform algebraic manipulations involving exponents and logarithms.
NEXT STEPS
  • Study the properties of logarithms in detail, focusing on product, quotient, and power rules.
  • Practice simplifying complex logarithmic expressions using various examples.
  • Explore the application of logarithms in calculus, particularly in differentiation and integration.
  • Learn about the change of base formula for logarithms and its applications.
USEFUL FOR

Students of calculus, mathematics educators, and anyone looking to strengthen their understanding of logarithmic functions and their applications in calculus.

thomasrules
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I tried this question and can't get it:

log subscript 3(9 times (9)^(1/5))
 
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realize that
[tex]9 \ * \ 9^\frac{1}{5} = 9^{1 + \frac{1}{5}} = 9^\frac{6}{5}[/tex]

Then use properties of logs
 
thank you stranger
 

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