Write the Expression as a Single Logarithm with Coefficient 1 $$\frac { 3 } { 2 } \log _ { n } 9 y + \frac { 9 } { 5 } \log _ { n } \left( 81 y ^ { 2 } \right)$$

question 369

Multiple Choice

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers.
- $$\frac { 3 } { 2 } \log _ { n } 9 y + \frac { 9 } { 5 } \log _ { n } \left( 81 y ^ { 2 } \right)$$

• A) \(\log _ { n } \left( 729 y ^ { 9 / 10 } \right)\)
• B) \(\log _ { n } ( 9^{39 / 20} y ^{63 / 40 })\)
• C) \(\log _ { n } \left( 9^{51 / 10} y ^ { 51 / 10 } \right)\)
• D) \(\log _ { n } \left( 729 \mathrm { y } ^ { 39 / 40 } \right)\)

Determine sample sizes needed for estimating population parameters within a specified margin of error.

Formulate null and alternative hypotheses for testing differences between population means and proportions.

Understand and apply the concept of p-values in hypothesis testing to make informed decisions.

Interpret the results and implications of hypothesis tests in context, including understanding Type I and II errors.

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