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  4. If log (x y3)=1, log (x2 y)=1, then the value of log (x y)5 is

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

Continuity and Differentiability

Solution:

$\log \left(x y^3\right)=1\,\,\,\,\,\, \log \left(x^2 y\right)=1$
$x y^3=10 \ldots \ldots(1) \,\,\,\,\, x^2 y=10$ .....(2)
$(1) \div(2) $
$y^2=x $
$y^5=10 \Rightarrow y=10^{1 / 5} $
$x=10^{2 / 5}$
$\log (x y)^5=\log \left(10^{3 / 5}\right)^5=3$