Question 75

$$\left(\frac{1}{2}\right) \log_{10} 25 - 2\log_{10} 3 + \log_{10} 18$$ equals

Solution

Expression : $$\left(\frac{1}{2}\right) \log_{10} 25 - 2\log_{10} 3 + \log_{10} 18$$

= $$\left(\frac{1}{2}\right) \log_{10} (5)^2 - 2\log_{10} 3 + \log_{10} (3^2\times2)$$

Using, $$\log (a\times b)=\log a+\log b$$ and $$\log a^b=b\log a$$

= $$\log_{10} 5-2\log_{10} 3+2\log_{10} 3+\log_{10} 2$$

= $$\log_{10} (5\times2)=\log_{10} 10=1$$

=> Ans - (B)

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