Subjects algebra

Log 891 E168C1

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **Problem Statement:** Calculate $\log 891$. 2. **Formula and Rules:** The logarithm $\log a$ (base 10) is the power to which 10 must be raised to get $a$. We can use factorization to simplify the calculation. 3. **Factorize 891:** $$891 = 9 \times 99 = 3^2 \times (9 \times 11) = 3^2 \times 3^2 \times 11 = 3^4 \times 11$$ 4. **Use logarithm properties:** $$\log(891) = \log(3^4 \times 11) = \log(3^4) + \log(11) = 4\log(3) + \log(11)$$ 5. **Approximate values:** $$\log(3) \approx 0.4771, \quad \log(11) \approx 1.0414$$ 6. **Calculate:** $$4 \times 0.4771 + 1.0414 = 1.9084 + 1.0414 = 2.9498$$ 7. **Final answer:** $$\log 891 \approx 2.9498$$