Given 3log X + 1/2log Y = 2, Express Y in Term of X.

Given 3log x + `1/2`log y = 2, express y in term of x.

Sum

3log x + `1/2`log y = 2
⇒ log x³ + log√y = 2
⇒ log x³√y = 2
⇒ x³√y = 10²⇒ √y = `10^2/x^3`
Squaring both sides, we get
y = `10000/x^6`

⇒ y = `10000x^-6`

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Expansion of Expressions with the Help of Laws of Logarithm

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Chapter 8: Logarithms - Exercise 8 (B) [Page 107]

Chapter 8 Logarithms
Exercise 8 (B) | Q 14 | Page 107

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

Simplify : log (a)³ - log a

Express the following in terms of log 5 and/or log 2: log250

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

Simplify the following:

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

If 2 log x + 1 = 40, find: log 5x

If log 2 = 0.3010, log 3 = 0.4771 and log 5 = 0.6990, find the values of: log45

If log 27 = 1.431, find the value of the following: log 9

If x² + y² = 6xy, prove that `"log"((x - y)/2) = (1)/(2)` (log x + log y)