Sure! Let's solve the given logarithmic expression step-by-step using the properties of logarithms.
We start with the given expression:
[tex]\[
\log_{15}\left(\frac{x}{y}\right)
\][/tex]
### Step 1: Use the Quotient Property of Logarithms
One of the key properties of logarithms is the quotient property, which states:
[tex]\[
\log_b\left(\frac{m}{n}\right) = \log_b(m) - \log_b(n)
\][/tex]
Here, we can identify [tex]\( m = x \)[/tex] and [tex]\( n = y \)[/tex], and apply this property to our expression:
[tex]\[
\log_{15}\left(\frac{x}{y}\right) = \log_{15}(x) - \log_{15}(y)
\][/tex]
### Step 2: Verify Simplification
We have:
[tex]\[
\log_{15}(x) - \log_{15}(y)
\][/tex]
In this case, since no specific values for [tex]\( x \)[/tex] and [tex]\( y \)[/tex] are provided, there is no further simplification possible from this point.
So, the simplified form of the given logarithmic expression using the quotient property of logarithms is:
[tex]\[
\log_{15}\left(\frac{x}{y}\right) = \log_{15}(x) - \log_{15}(y)
\][/tex]
This is the final answer.
