Question

Write the logarithmic equation for: 

V = `(1)/("D"l) sqrt("T"/(pi"r")`

Answer 1

V = `(1)/("D"l) sqrt("T"/(pi"r")`

⇒ V = `(1)/("D"l)("T"/(pi"r"))^(1/2)`
Considering log on both the sides, we get

log V = `"log"[(1)/("D"l)("T"/(pi"r"))^(1/2)]`

= `"log"(1/("D"l)) + "log"("T"/(pi"r"))^(1/2)`

= `("log"1 - "log""D" - "log"l) + (1)/(2)"log"("T"/(pi"r"))`

= `(0 - "log""D" - "log"l) + (1)/(2)("log""T" - "log"pi - "log""r")`

= `(1)/(2)("log""T" - "log"pi - "log""r") - "log""D" - "log"l`.