Question

if log s-log pie =2log2+2logr,express the relation between s and r free from logarithms

Answer 1

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HERE'S THE ANSWER

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♠️ We'll be using three important formulas of logarith

✔️$\blue{ log(a) - log(b)\:=\:log(a/b)}$

✔️$\blue{ log(a) + log(b)\:=\:log(ab)}$

✔️$\blue{ e^{log(x)}\:= x}$

✔️$\blue{ n log(x)\:= log(x^{n})}$

♠️ $\bold{ log(s) - log(\pi)\:=\:2log(2)+2log(r)}$

=>$\bold{ log(s) - log(\pi)\:=\:2(log(2)+log(r))}$

⏺️ Using properties

=>$\bold{ log(s/ \pi)\:=\:2(log(2r))}$

=>$\bold{ log(s/ \pi)\:=\:(log(2r)^{2})}$

=> $\bold{ log(s/ \pi)\:=\:(log 4(r)^{2})}$

⏺️ Taking antilog or ( e ) both sides

=> $\bold{ e^{log(s/ \pi)}\:=\:e^{(log 4(r)^{2})}}$

=> $\bold{ s/ \pi \:=\:4(r)^{2}}$

=> $\boxed{ s\:= 4 \pi r^{2}}$

HOPE HELPED...

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Answer 2

log s-log pie =2log2+2logr

log(s/π) = 2 ( log 2 + log r )

log (s/π) = 2log(2r)

log(s/π) = log ( 2r)^2

log(s/π) = log ( 4 r^2 )

s/π = 4 r^2

s = 4 π r^2