Question

If $x=\log 0.6$, $y=\log 1.25$ and $z=\log 3-2\log 2$, then the value of $x+y-z$ is equal to

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is A $0$

$x=\log 0.6$; $y=\log 1.25$; $z=\log 3-2\log 2$

$x+y-z=\log 0.6+\log 1.25-(\log 3-2\log 2)$

$\therefore x+y-z=\log (0.6\times 1.25)-\log \frac{3}{4}$ ...($\log \frac{a}{b}=\log a-\log b$ and $\log (a\cdot b)=\log a+\log b$)

$\therefore x+y-z=\log 0.75-\log 0.75=0$