How can the properties of logarithms be used to simplify and solve equations?

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SUMMARY

The discussion focuses on utilizing the properties of logarithms to simplify expressions and solve equations. A participant successfully transformed the expression into "ln(x) - 1/2ln(x^2 + 1)" but encountered difficulties with another expression involving a denominator. The conversation emphasizes the importance of understanding logarithmic identities, such as the product and quotient rules, to effectively manipulate logarithmic expressions.

PREREQUISITES
  • Understanding of logarithmic properties, including product, quotient, and power rules.
  • Familiarity with algebraic manipulation techniques.
  • Basic knowledge of natural logarithms and their applications.
  • Ability to solve equations involving logarithmic functions.
NEXT STEPS
  • Study the product and quotient rules of logarithms in detail.
  • Practice simplifying complex logarithmic expressions using examples.
  • Explore applications of logarithms in solving exponential equations.
  • Learn about the change of base formula for logarithms.
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Students, educators, and anyone looking to enhance their understanding of logarithmic functions and their applications in algebra and calculus.

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Use the properties of Logarithms to write the expression as a sum, difference, and/or constant multiple of logarithms:
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What have you tried? Where are you stuck?
 
Ackbach said:
What have you tried? Where are you stuck?

For the first one I did " lnx-1/2ln(x^2+1)"

For the second one, I have no idea what to do :(
 
What should you do with the denominator? How about the product in the numerator?
 

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