Write the Logarithmic Equation For: F = "G"("M"_1"M"_2)/"D"^2

Write the logarithmic equation for:

F = `"G"("m"_1"m"_2)/"d"^2`

Sum

F = `"G"("m"_1"m"_2)/"d"^2`
Considering log on both the sides, we get

logF = `"log"("G"("m"_1"m"_2)/"d"^2)`

= log (Gm₁m₂) - log d²
= logG + logm₁ + logm₂ - 2 log d.

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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 4.1

Given 2 log₁₀ x + 1 = log₁₀ 250, find :
(i) x
(ii) log₁₀ 2x

Prove that : If a log b + b log a - 1 = 0, then b^a. a^b = 10

Express the following in terms of log 5 and/or log 2: log500

Express the following as a single logarithm:
log 18 + log 25 - log 30

Express the following as a single logarithm:

`2"log" (16)/(25) - 3 "log" (8)/(5) + "log" 90`

Simplify the following:

`2 "log" 5 +"log" 8 - (1)/(2) "log" 4`

If log 16 = a, log 9 = b and log 5 = c, evaluate the following in terms of a, b, c: log 720

If log a = p and log b = q, express `"a"^3/"b"^2` in terms of p and q.

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

If x² + y² = 7xy, prove that `"log"((x - y)/3) = (1)/(2)` (log x + log y)