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

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

Given: log₃ m = x and log₃ n = y.
Express 3^{2x - 3} in terms of m.

Given `log_x 25 - log_x 5 = 2 - log_x (1/125)` ; find x.

Write the logarithmic equation for:

n = `sqrt(("M"."g")/("m".l)`

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`2"log"(9)/(5) - 3"log"(3)/(5) + "log"(16)/(20)`

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 12

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

Simplify: log a² + log a^-1

Find the value of:

`("log"sqrt125 - "log"sqrt(27) - "log"sqrt(8))/("log"6 - "log"5)`