Question

If $x=\log 0.6$, $y=\log 1.25$ and $z=\log 3-2\log 2$, then the value of $5^{x+y-z}$ is equal to

• A. $7$
• B. $0$
• C. $1$
• D. $2$

Answer 1

The correct option is C $1$

$x=\log 0.6=\log \frac{6}{10}=\log \frac{3}{5}=\log 3-\log 5$

$y=\log 1.25=\log \frac{125}{100}=\log \frac{5}{4}=\log 5-\log 4=\log 5-2\log 2$

$z=\log 3-2\log 2$

Now, $x+y-z=\log 3-\log 5+\log 5-2\log 2-(\log 3-2\log 2)=0$

And $5^{x+y-z}=5^0=1$