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Use the properties of logarithms to expand [tex]\log \frac{x^4}{y}[/tex].

Each logarithm should involve only one variable and should not have any exponents or fractions. Assume that all variables are positive.

[tex]\log \frac{x^4}{y} = \log x^4 - \log y = 4\log x - \log y[/tex]

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GinnyAnsweridn
To expand the expression [tex]\(\log \frac{x^4}{y}\)[/tex] using the properties of logarithms, we can follow these steps:

1. Property of Logarithms - Quotient Rule: The logarithm of a quotient is the difference of the logarithms. In this case:

[tex]\[\log \frac{x^4}{y} = \log(x^4) - \log(y)\][/tex]

2. Property of Logarithms - Power Rule: The logarithm of a power is the exponent times the logarithm of the base. So, we apply this property to [tex]\(\log(x^4)\)[/tex]:

[tex]\[\log(x^4) = 4 \log(x)\][/tex]

3. Combining the results from the steps above, we have:

[tex]\[\log \frac{x^4}{y} = 4 \log(x) - \log(y)\][/tex]

So the fully expanded form is:

[tex]\[ \log \frac{x^4}{y} = 4 \log(x) - 1 \log(y) \][/tex]
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