If 2 Log Y - Log X - 3 = 0, Express X in Terms of Y.

If 2 log y - log x - 3 = 0, express x in terms of y.

Sum

2log - logx - 3 = 0
⇒ logx = 2logy - 3
⇒ logx = logy²- 3log10 ...[∵ log10 = 1]
⇒ logx = logy²- log10³
⇒ logx = `"log"(y^2/1000)`
∴ x = `y^2/(1000)`.

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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 20

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

If log 27 = 1.431, find the value of : log 300

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

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

Express the following in terms of log 2 and log 3: `"log" root(3)(144)`

Express the following in terms of log 2 and log 3: `"log"root(5)(216)`

Express the following as a single logarithm:

`2"log"(15)/(18) - "log"(25)/(162) + "log"(4)/(9)`

Simplify the following:

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

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

Find the value of:

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