Question

\((\frac{1}{2})\) log₁₀ 25-2log₁₀ 3 + log₁₀ 18 equals

• A. 18
• B. 1
• C. log₁₀3
• D. None of these

Answer 1

The Correct Option is B

The correct option is (B): 1
Explanation: To simplify the expression \((\frac{1}{2}) \log_{10} 25 - 2 \log_{10} 3 + \log_{10} 18\), we can follow these steps:
Use the properties of logarithms:
- \(\log_{10} 25 = \log_{10} (5^2) = 2 \log_{10} 5\)
  - Therefore, \((\frac{1}{2}) \log_{10} 25 = \frac{1}{2} (2 \log_{10} 5) = \log_{10} 5\)
Apply the property for \(2 \log_{10} 3\):
  - \(2 \log_{10} 3 = \log_{10} (3^2) = \log_{10} 9\)
Combine the logs:
  \[\log_{10} 5 - \log_{10} 9 + \log_{10} 18\]
Using the properties of logarithms:
  \[= \log_{10} \left(\frac{5 \times 18}{9}\right) = \log_{10} \left(\frac{90}{9}\right) = \log_{10} 10\]
Final Result:
  \[\log_{10} 10 = 1\]
Thus, the final answer is 1.