Question

choose the single logarithmic expression that is equivalent to the one shown.

log z - log y

a. log(y - z)
b. log(x - y)
c. log z/y
d. log y/z

Answer 1

C is th E answer of the question

Answer 2

Answer:

The logarithmic expression which is equal to the expression $\log z - \log y$ is $\log \left( \frac { z } { y } \right)$

Solution:

According to the logarithmic principles, We know that,

$\log a - \log b = \log \frac { a } { b }$

$\begin{array} { c } { \log a + \log b = \log a b } \\\\ { \log a ^ { n } = n \log a } \end{array}$

Hence, the given logarithmic expression is in the form of subtraction

Here, in the logarithmic principles, the subtraction of two logs will lead to its division.

$\log z - \log y = \log \frac { z } { y }$

Thus, the logarithmic expression which is equal to the given expression $\log z - \log y$ is $\log \left( \frac { z } { y } \right)$. Hence, the answer is option C.