Question

Very urgent !

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Answer 1

$\large\underline{\sf{Solution-}}$

Properties of Logarithmic :-

$\rm :\longmapsto\: log(xy) = logx + logy$

$\rm :\longmapsto\:log\bigg(\dfrac{x}{y} \bigg) = logx - logy$

$\rm :\longmapsto\: log( {x}^{y} ) = y \: logx$

Part - (i)

$\rm :\longmapsto\:PV = K$

Taking log on both sides,

$\rm :\longmapsto\:log(PV) =log K$

$\rm :\longmapsto\:logP + logV=log K$

Part - (ii)

$\rm :\longmapsto\:V = \dfrac{\pi \: Pr}{8 \eta \: l}$

Taking log on both sides,

$\rm :\longmapsto\: \: logV = log \bigg(\dfrac{\pi \: Pr}{8 \eta \: l} \bigg)$

$\rm :\longmapsto\:logV = log\pi + logP + logr - log8 - log \eta - logl$

$\rm :\longmapsto\:logV = log\pi + logP + logr - log {2}^{3} - log \eta - logl$

$\rm :\longmapsto\:logV = log\pi + logP + logr - 3log {2} - log \eta - logl$

Part - (iii)

$\rm :\longmapsto\:h = \dfrac{2T}{r \rho \: g}$

Taking log on both sides,

$\rm :\longmapsto\:logh = log \bigg(\dfrac{2T}{r \rho \: g} \bigg)$

$\rm :\longmapsto\:logh = log2 + logT - logr - log \rho \: - logg$

Part - (iv)

$\rm :\longmapsto\:T = 2\pi \sqrt{\dfrac{I}{ \alpha } }$

Taking log on both sides,

$\rm :\longmapsto\:logT = log(2\pi \sqrt{\dfrac{I}{ \alpha } } )$

$\rm :\longmapsto\:logT = log2\pi \: + log \sqrt{\dfrac{I}{ \alpha } }$

$\rm :\longmapsto\:logT = log2 + log\pi \: + log \bigg(\dfrac{I}{ \alpha } \bigg)^{ \dfrac{1}{2} }$

$\rm :\longmapsto\:logT = log2 + log\pi \: +\dfrac{1}{2} log \bigg(\dfrac{I}{ \alpha } \bigg)$

$\rm :\longmapsto\:logT = log2 + log\pi \: +\dfrac{1}{2} \bigg(logI - log\alpha \bigg)$

Answer 2

Answer:

Hello palsabita

How are you