Sure, let's simplify the given expression using the properties of logarithms. Remember, log(x/y^n) can be rewritten using the rule log(a) - log(b) to get log(a) - log(b^n), and then we can apply another rule, log(a^n) = n*log(a), to simplify it even more.
In the given expression, we have log(x/y^7).
Step 1: Using the property of logarithms that log(a/b) = log(a) - log(b), we can rewrite the given expression as:
log(x) - log(y^7)
Step 2: Then, we apply the property of logarithms that log(a^n) = n*log(a), which allows us to further simplify the expression as:
log(x) - 7 * log(y)
Finally, we have an expanded form of the given expression, which is:
log(x) - 7*log(y)
By these steps, we expanded the logarithm expression with a variable x and y to the power of 7 in the denominator to a simpler form, where no variable has an exponent anymore.