Evaluate each logarithm by using properties of logarithms and the following facts.
loga(x) = 5.4
  
loga(y) = 1.6
  
loga(z) = 2.4 (d)    
loga(

y
)


It seems you're asking to evaluate logarithms using the given values for \(\log_a(x)\), \(\log_a(y)\), and \(\log_a(z)\). You provided:

- \(\log_a(x) = 5.4\)
- \(\log_a(y) = 1.6\)
- \(\log_a(z) = 2.4\)

However, the last part of your query is incomplete. Could you clarify or complete what you need to evaluate for \(\log_a(y)\)?

If you meant just \(\log_a(y)\), it is already provided as \(1.6\). Otherwise, feel free to correct or add further details for the part you'd like to evaluate, and I'll proceed with solving it.

Would you like to see how the properties of logarithms (like product, quotient, or power rules) are used in evaluating combined logarithmic expressions?

Here are five follow-up questions related to logarithmic properties:
1. How would you apply the product rule for logarithms: \(\log_a(xy)\)?
2. How do you simplify the quotient of two logarithmic expressions: \(\log_a\left(\frac{x}{y}\right)\)?
3. How would you use the power rule to simplify \(\log_a(x^2)\)?
4. What is the relationship between logarithmic and exponential functions?
5. How would you solve \(\log_a(xy^2)\) using the given values of \(\log_a(x)\) and \(\log_a(y)\)?

**Tip:** The power rule for logarithms states \(\log_b(x^n) = n \log_b(x)\), making it useful for simplifying expressions involving exponents.

Evaluate each logarithm by using properties of logarithms and the following facts: loga(x) = 5.4, loga(y) = 1.6, loga(z) = 2.4 (d) loga(y).

This page explains how to evaluate logarithms using properties like the product, quotient, and power rules. Given loga(x) = 5.4, loga(y) = 1.6, and loga(z) = 2.4, learn how to simplify expressions such as loga(xy) or loga(x/y) using these values. Suitable for students in Grades 9-11.

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