Assume That X, Y, Z and B Are Positive Numbers $\log _ { b } \sqrt [ 4 ] { \frac { x ^ { 5 } y ^ { 2 } } { z ^ { 4 } } }$

question 197

Multiple Choice

Assume that x, y, z and b are positive numbers.Use the properties of logarithms to write the expression $\log _ { b } \sqrt [ 4 ] { \frac { x ^ { 5 } y ^ { 2 } } { z ^ { 4 } } }$ in terms of the logarithms of x, y, and z.

• A) \(\frac { 5 } { 4 } \log _ { b } x + \log _ { b } y - \log _ { b } z\)
• B) \(\frac { 5 } { 4 } \log _ { b } x + \frac { 1 } { 2 } \log _ { b } y - \log _ { b } z\)
• C) \(\log _ { b } x + \frac { 1 } { 2 } \log _ { b } y - \log _ { b } z\)
• D) \(\frac { 5 } { 4 } \log _ { b } ( x + y + z )\)
• E) \(20 \log _ { b } x + 8 \log _ { b } y - 16 \log _ { b } z\)

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