Use the Properties of Logarithms to Rewrite the Expression $$\log _ { b } \sqrt [ 3 ] { \frac { x ^ { 2 } } { y ^ { 4 } z ^ { 7 } } }$$

question 187

Multiple Choice

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent
positive real numbers.
- $$\log _ { b } \sqrt [ 3 ] { \frac { x ^ { 2 } } { y ^ { 4 } z ^ { 7 } } }$$

• A) \(2 \log _ { b } x - 4 \log _ { b } y - 7 \log _ { b } z\)
• B) \(\frac { 2 } { 3 } \log _ { b } x - \frac { 4 } { 3 } \log _ { b } y - \frac { 7 } { 3 } \log _ { b } z\)
• C) \(\frac { 1 } { 3 } \log _ { b } x ^ { 2 } - \log _ { b } y ^ { 4 } - \log _ { b } z ^ { 7 }\)
• D) \(\frac { 2 } { 3 } \log _ { b } x \div \left( \frac { 4 } { 3 } \log _ { b } y \cdot \frac { 7 } { 3 } \log _ { b } z \right)\)

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Definitions:

Levator Ani

A broad, thin muscle situated on either side of the pelvis, part of the pelvic floor, that supports pelvic viscera and provides sphincter-like action in the anal canal and vagina.

Pelvic Viscera

Internal organs located within the pelvic cavity, including the bladder, rectum, and for females, the uterus and ovaries.

Urination

The process of excreting urine from the urinary bladder through the urethra to the external urinary orifice, regulated by voluntary and involuntary muscle controls.

Erection

The process by which erectile tissue becomes enlarged and firm, typically in response to sexual excitement.