How Do You Solve Logarithmic Expressions Involving Fractions?

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SUMMARY

The discussion focuses on solving the logarithmic expression log_2(15/2) using the known values log_2(5) = x and log_2(3) = y. The correct expression for log_2(15/2) is derived as log_2(15) - log_2(2). By applying the properties of logarithms, specifically log_2(15) can be expressed as log_2(5) + log_2(3), leading to the conclusion that log_2(15/2) = x + y - 1. Therefore, the correct answer is option D: x + y - 1.

PREREQUISITES
  • Understanding of logarithmic properties, specifically the quotient and product rules.
  • Familiarity with base-2 logarithms (log_2).
  • Basic algebraic manipulation skills.
  • Knowledge of fractions and their representation in logarithmic form.
NEXT STEPS
  • Study the properties of logarithms, including the product, quotient, and power rules.
  • Practice solving logarithmic equations involving multiple variables.
  • Explore logarithmic identities and their applications in algebra.
  • Learn how to convert between different logarithmic bases, such as using the change of base formula.
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Students in algebra, educators teaching logarithmic concepts, and anyone looking to enhance their problem-solving skills in logarithmic expressions.

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If [tex]log_2 (5)[/tex] = x and [tex]log_2 (3)[/tex] = y , determine an expression for [tex]log_2 (15/2)[/tex], in terms of x and y.
A. xy
B. x + y
C. xy - 1
D. x + y - 1

I'm suppose to solve this by hand but it doesn't seem possible. I tried so many ways but the does not come out as D. which is the answer Can someone explain the steps to this problem? Thanks!
 
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Hint: log2(15/2) = log2(15) - log2(2)
 

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