Write the Logarithmic Equation For: V = 4 3 π R 3

Write the logarithmic equation for:

V = `(4)/(3)pi"r"^3`

Sum

V = `(4)/(3)pi"r"^3`
Considering log on both the sides, we get

log V = `"log"(4/3 pi"r"^3)`

= log4 + logπ + logr³ - log3
= log2² + logπ + 3logr - log3
= 2log2 - log3 + logπ + 3logr.

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Expansion of Expressions with the Help of Laws of Logarithm

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Chapter 10: Logarithms - Exercise 10.2

Chapter 10 Logarithms
Exercise 10.2 | Q 4.4

If log 2 = 0.3010 and log 3 = 0.4771 ; find the value of : log 1.2

Express the following in terms of log 2 and log 3: log 36

Express the following in terms of log 2 and log 3: log 54

Express the following in terms of log 2 and log 3: log12⁸

Express the following in terms of log 2 and log 3: `"log"(225)/(16) - 2"log"(5)/(9) + "log"(2/3)^5`

Express the following as a single logarithm:

`2 "log" 3 - (1)/(2) "log" 16 + "log" 12`

Simplify the following:

`3"log" (32)/(27) + 5 "log"(125)/(24) - 3"log" (625)/(243) + "log" (2)/(75)`

If log 16 = a, log 9 = b and log 5 = c, evaluate the following in terms of a, b, c: log 12

If log 2 = 0.3010, log 3 = 0.4771 and log 5 = 0.6990, find the values of: `"log" sqrt(72)`

If log 8 = 0.90, find the value of each of the following: `"log"sqrt(32)`