Assume that x , y , and b ( b ≠ 1) are positive numbers. Use the properties of logarithms to write the expression in terms of the logarithms of x and y .

Question

Quizplus · Accepted Answer

Using the logarithmic property of product, we can write $\log_b(xy) = \log_b(x)+\log_b(y)$. Thus, the expression can be written as $\frac{\log_b(x)-\log_b(y)}{-\log_b(x)+\log_b(y)} = \frac{\log_b(y)-\log_b(x)}{\log_b(y)-\log_b(x)}\cdot\frac{\log_b(x)}{\log_b(y)} = -\frac{\log_b(x)}{\log_b(y)}$. Therefore, the answer is (D).

Assume That X , Y , and B ( B