Question

1/2 log 10 25-2 log 10 3 + log 10 18

Answer 1

Step-by-step explanation:

$\frac{1}{2} log_{10}25 - 2log_{10}3 + log_{10}18 \\ = log_{10} {(25)}^{ \frac{1}{2} } - log_{10} {3}^{2} + log_{10}18 \\= log_{10} \sqrt{25} - log_{10} 9 + log_{10}18 \\= log_{10} 5 + log_{10}18 - log_{10} 9 \\ = log_{10} \{ 5 \times 18\}- log_{10} 9 \\ = log_{10} 90 - log_{10} 9 \\ = log_{10} \frac{90}{9} \\ = log_{10} 10 \\ = 1 \\ Thus \\ \frac{1}{2} log_{10}25 - 2log_{10}3 + log_{10}18 = 1$