Question

If $x=1+\log 2-\log 5,y=2\log 3$ and $z=\log a-\log 5$, then the value of $a$, if $x+y=2z$ is

• A. $20$
• B. $30$
• C. $40$
• D. $50$

Answer 1

Answer: (B)

$30$

$x=1+\log 2-\log 5;y=2\log 3$; $z=\log a-\log 5$

$x+y=2z$ ......(Given)

$\therefore 1+\log 2-\log 5+2\log 3=2(\log a-\log 5)$

$\therefore \log 4+\log 9=\log (\frac{a}{5}{)}^2$ ....($\log \frac{a}{b}=\log a-\log b$ and $\log a^b=b\log a$)

$\therefore 4\times 9=(\frac{a}{5}{)}^2$

$\therefore a=2\times 3\times 5=30$