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Question
Write the logarithmic equation for:
V = `(1)/("D"l) sqrt("T"/(pi"r")`
Sum
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Solution
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`.
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Expansion of Expressions with the Help of Laws of Logarithm
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