Use the Properties of Logarithms to Write the Expression $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$

question 39

Multiple Choice

Use the properties of logarithms to write the expression $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$ as a sum, difference, or multiple of logarithms. Assume x and y are positive numbers. Simplify if possible.

• A) \(1 + \log _ { 4 } 9 x - \log _ { 4 } y\)
• B) \(1 + 9 \log _ { 4 } x - \log _ { 4 } y\)
• C) \(\log _ { 4 } 36 + \log _ { 4 } x - \log _ { 4 } y\)
• D) \(\log _ { 4 } 1 + 9 \log _ { 4 } x + \log _ { 4 } y\)

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Definitions:

Borrowed

Money that one has taken on loan from another party, under the condition that it will be repaid, usually with interest, at a later date.

Interest

The charge for borrowing money or the return on invested capital, usually expressed as an annual percentage rate.

Interest Rate

The fraction of a borrowed sum that incurs interest charges for the borrower, often expressed in terms of a yearly percentage.

Investment

The process of assigning financial resources with the goal of making a profit or gaining income.