Question

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

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

Answer 1

Answer: (B)

1

Answer 2

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.