Subjects algebra

Log Base Seven Eea6Cc

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1. **State the problem:** Evaluate $\log_7 \left( \frac{1}{7} \right)$. 2. **Recall the definition of logarithm:** $\log_b a = c$ means $b^c = a$. Here, $b=7$ and $a=\frac{1}{7}$. 3. **Rewrite the fraction:** $\frac{1}{7} = 7^{-1}$. 4. **Apply the definition:** We want to find $c$ such that $7^c = 7^{-1}$. 5. **Since the bases are equal, the exponents must be equal:** $c = -1$. 6. **Therefore,** $\log_7 \left( \frac{1}{7} \right) = -1$.