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.

बेरीज

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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पाठ 10: Logarithms - Exercise 10.2

पाठ 10 Logarithms
Exercise 10.2 | Q 20

If x = (100)^a , y = (10000)^b and z = (10)^c , find log`(10sqrty)/( x^2z^3)` in terms of a, b and c.

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

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Express the following in terms of log 5 and/or log 2: log160

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

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

If log₁₀25 = x and log₁₀27 = y; evaluate without using logarithmic tables, in terms of x and y: log₁₀3

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