Question
Write the logarithmic equation for:$V =\frac{1}{ D l} \sqrt{\frac{ T }{\pi r }}$
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Answer
$V =\frac{1}{ D l} \sqrt{\frac{ T }{\pi r }}$
$\Rightarrow V =\frac{1}{ D l}\left(\frac{ T }{\pi r }\right)^{\frac{1}{2}}$
Considering $\log$ on both the sides, we get
$\log V =\log \left[\frac{1}{ D l}\left(\frac{ T }{\pi r }\right)^{\frac{1}{2}}\right] $
$=\log \left(\frac{1}{ D l}\right)+\log \left(\frac{ T }{\pi r }\right)^{\frac{1}{2}} $
$=(\log 1-\log D -\log l)+\frac{1}{2} \log \left(\frac{ T }{\pi r }\right) $
$=(0-\log D -\log l)+\frac{1}{2}(\log T -\log \pi-\log r )$
$=\frac{1}{2}(\log T -\log \pi-\log r )-\log D -\log l .$
$\Rightarrow V =\frac{1}{ D l}\left(\frac{ T }{\pi r }\right)^{\frac{1}{2}}$
Considering $\log$ on both the sides, we get
$\log V =\log \left[\frac{1}{ D l}\left(\frac{ T }{\pi r }\right)^{\frac{1}{2}}\right] $
$=\log \left(\frac{1}{ D l}\right)+\log \left(\frac{ T }{\pi r }\right)^{\frac{1}{2}} $
$=(\log 1-\log D -\log l)+\frac{1}{2} \log \left(\frac{ T }{\pi r }\right) $
$=(0-\log D -\log l)+\frac{1}{2}(\log T -\log \pi-\log r )$
$=\frac{1}{2}(\log T -\log \pi-\log r )-\log D -\log l .$
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