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प्रश्न
Given log x = 2m - n , log y = n - 2m and log z = 3m - 2n , find in terms of m and n, the value of log `(x^2y^3 ) /(z^4) `.
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उत्तर
Given log x = 2m - n, log y = n - 2m, log z = 3m - 2n.
Given : log `(x^2y^3)/(z^4)`
We know that log(a/b) = log a - log b.
⇒ log `(x^2y^3)` - log `(z^4)`
We know that log(ab) = log a + log b
⇒ log `(x^2)` + log `(y^3)` - log `(z^4)`
⇒ 2 log x + 3 log y - 4 log z
⇒ 2(2m - n) + 3(n - 2m) - 4(3m - 2n)
⇒ 4m - 2n + 3n - 6m - 12m + 8n
⇒ -14m + 9n
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