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

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

If 3( log 5 - log 3 ) - ( log 5 - 2 log 6 ) = 2 - log x, find x.

If log₁₀2 = a and log₁₀3 = b ; express each of the following in terms of 'a' and 'b': log 2.25

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

If log 2 = 0.3010 and log 3 = 0.4771; find the value of : log 15

If log₁₀ 8 = 0.90; find the value of : log√32

Prove that : (log a)² - (log b)² = log `(( a )/( b ))` . Log (ab)

Express the following in terms of log 2 and log 3: log 144

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

If log 27 = 1.431, find the value of the following: log300

Find the value of:

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