Given,
⇒ R = 3 V π h Taking log on Both sides, ⇒ log R = log 3 V π h ⇒ log R = log ( 3 V π h ) 1 2 ⇒ log R = 1 2 log ( 3 V π h ) ⇒ log R = 1 2 ( log 3 V − log π h ) ⇒ log R = 1 2 [ log 3 + log V − ( log π + log h ) ] ⇒ log R = 1 2 ( log 3 + log V − log π − log h ) \Rightarrow R = \sqrt {\dfrac{3V}{\pi h}} \\[1em] \text{Taking log on Both sides,} \\[1em] \Rightarrow \log \space R = \log \space {\sqrt{\dfrac{3V}{\pi h}}} \\[1em] \Rightarrow \log \space R = \log \space {\Big(\dfrac{3V}{\pi h}\Big)}^{\dfrac{1}{2}} \\[1em] \Rightarrow \log \space R = \dfrac{1}{2} \log \space {\Big(\dfrac{3V}{\pi h}\Big)} \\[1em] \Rightarrow \log \space R = \dfrac{1}{2} (\log \space {3V} - \log \space {\pi h}) \\[1em] \Rightarrow \log \space R = \dfrac{1}{2} [\log \space {3} + \log \space {V} - (\log \space {\pi} + \log \space { h})] \\[1em] \Rightarrow \log \space R = \dfrac{1}{2} (\log \space {3} + \log \space {V} - \log \space {\pi} - \log \space { h}) ⇒ R = πh 3 V Taking log on Both sides, ⇒ log R = log πh 3 V ⇒ log R = log ( πh 3 V ) 2 1 ⇒ log R = 2 1 log ( πh 3 V ) ⇒ log R = 2 1 ( log 3 V − log πh ) ⇒ log R = 2 1 [ log 3 + log V − ( log π + log h )] ⇒ log R = 2 1 ( log 3 + log V − log π − log h )
Hence, logarithmic equation is log R = 1 2 ( log 3 + log V − log π − log h ) \log \space R = \dfrac{1}{2} (\log \space {3} + \log \space {V} - \log \space {\pi} - \log \space { h}) log R = 2 1 ( log 3 + log V − log π − log h )
