4) Use properties of logarithms to evaluate the expression. Assume all expressions exist and are well-defined. $$ \log _{w} w^{11}-\log _{w} w^{2} $$

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To evaluate the expression $$ \log_{w} w^{11} - \log_{w} w^{2} $$, we can use the properties of logarithms.

1. **Apply the Power Rule of Logarithms**: The power rule states that $$ \log_{b} (a^{c}) = c \cdot \log_{b} a $$. In our case, since the base and the argument are the same, we can simplify each logarithm:

$$
   \log_{w} w^{11} = 11 \cdot \log_{w} w
   $$
   $$
   \log_{w} w^{2} = 2 \cdot \log_{w} w
   $$

Since $$ \log_{w} w = 1 $$ (because any logarithm of a number to its own base is 1), we can simplify further:

$$
   \log_{w} w^{11} = 11 \cdot 1 = 11
   $$
   $$
   \log_{w} w^{2} = 2 \cdot 1 = 2
   $$

2. **Substitute Back into the Expression**: Now we can substitute these values back into the original expression:

$$
   \log_{w} w^{11} - \log_{w} w^{2} = 11 - 2
   $$

3. **Perform the Final Calculation**:

$$
   11 - 2 = 9
   $$

Thus, the value of the expression $$ \log_{w} w^{11} - \log_{w} w^{2} $$ is $$ 9 $$.
The expression $$ \log_{w} w^{11} - \log_{w} w^{2} $$ simplifies to 9.

4) Use properties of logarithms to evaluate the expression. Assume all expressions exist and are well-defined. \( \log _{w} w^{11}-\log _{w} w^{2} \)

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