Given: Log3 M = X and Log3 N = Y. Express 32x - 3 in Terms of M. - Mathematics

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

Sum

Given that log₃m = x and log₃n = y
⇒ 3^x = m and 3^y = n

Consider the given expression :
3^{2x - 3}
= 3^2x . 3^-3=` 3^(2x) . 1/3^3`

= `3^(2x)/3^3`

= `(3^x)^2/3^3`

= `m^2/27`
Therefore, 3^{2x - 3}= `m^2/27`

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Expansion of Expressions with the Help of Laws of Logarithm

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Chapter 8: Logarithms - Exercise 8 (C) [Page 108]

Chapter 8 Logarithms
Exercise 8 (C) | Q 5.1 | Page 108

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