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

• A. $0$
• B. $2$
• C. $1$
• D. $3$

Answer 1

Answer: (C)

$1$

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

$5^{x+y-z}=5^a$ where $a=x+y-z$

$a=\log 0.6+\log 1.25-(\log 3-2\log 2)$

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

$\therefore a=\log 0.75-\log 0.75=0$

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