Question

If $a=1+\log 2-\log 5$, $b=2\log 3$, $c=\log P-\log 5$ and $a+b=2c,$ then the value of $P$ will be

• A. $10$
• B. $20$
• C. $30$
• D. $40$

Answer 1

Answer: (C)

$30$

$a+b=2c\text{Sub value of a,b,c}1+\log 2-\log 5+2\log 3=2(\log P-\log 5)\log \left(\frac{10\times 2\times 3\times 3}{5}\right)=\log {\left(\frac{P}{5}\right)}^2\log (2^2\times 3^2)=\log \left(\frac{P^2}{5^2}\right)\text{Removing log}{P}^2=2^2{\times 3}^2{\times 5}^{2}P=2\times 3\times 5=30$