Question

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

• A. $<0$
• B. $>0$
• C. $>1$
• D. $<1$

Answer 1

The correct option is A $<0$

$x=\log 0.6=\log \frac{6}{10}=\log \frac{3}{5}=\log 3-\log 5$
$y=\log 1.25=\log \frac{125}{100}=\log \frac{5}{4}=\log 5-\log 4$
Now, $x+y=\log 3-\log 5+\log 5-\log 4=\log 3-\log 4=\log \frac{3}{4}=\log \frac{75}{100}=\log 0.75$