Question

If $\log \left(x{y}^3\right)=1,\log \left(x^{2}y\right)=1$, then the value of $\log (xy{)}^5$ is

• A. 1
• B. 3
• C. 5
• D. 7

Answer 1

Answer: (B)

$\log \left(x{y}^3\right)=1\log \left(x^{2}y\right)=1$
$x{y}^3=10\dots \dots (1)x^{2}y=10$ .....(2)
$(1)÷(2)$
$y^2=x$
$y^5=10\Rightarrow y=10^{1/5}$
$x=10^{2/5}$
$\log (xy{)}^5=\log {\left(10^{3/5}\right)}^5=3$