Find the value of each logarithmic expression. (Note: There's only one answer for the pair of logarithmic expressions indicated below.) $$ \log _{7} 7^{5} $$ and $$ 5 \cdot \log _{7} 7 $$

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To find the value of the logarithmic expressions $$ \log_{7} 7^{5} $$ and $$ 5 \cdot \log_{7} 7 $$, we can evaluate each expression separately.

1. **Evaluating $$ \log_{7} 7^{5} $$**:
   Using the property of logarithms that states $$ \log_{b} b^{x} = x $$, we have:
   $$
   \log_{7} 7^{5} = 5
   $$

2. **Evaluating $$ 5 \cdot \log_{7} 7 $$**:
   Again, using the property of logarithms, we know that $$ \log_{b} b = 1 $$. Therefore:
   $$
   \log_{7} 7 = 1
   $$
   Thus,
   $$
   5 \cdot \log_{7} 7 = 5 \cdot 1 = 5
   $$

Both expressions evaluate to the same value:
$$
\log_{7} 7^{5} = 5 \quad \text{and} \quad 5 \cdot \log_{7} 7 = 5
$$

Therefore, the value of each logarithmic expression is $$ \boxed{5} $$.
The value of each logarithmic expression is 5.

Find the value of each logarithmic expression. (Note: There's only one answer for the pair of logarithmic expressions indicated below.) \( \log _{7} 7^{5} \) and \( 5 \cdot \log _{7} 7 \)

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