Given that log m = x + y and log n = x - y, express the value of log m 2 n in terms of x and y.

Given, log m = x + y .......(i) log n = x - y ........(ii) Multiplying (i) by 2 we get, 2log m = log m 2 = 2x + 2y ......(iii) Adding (ii) and (iii) we get, ⇒ log m 2 + log n = 2x + 2y + (x - y) ⇒ log m 2 n = 3x + y. Hence, log m 2 n = 3x + y.

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Mathematics

Given that log m = x + y and log n = x - y, express the value of log m²n in terms of x and y.

Logarithms

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Answer

Given,

log m = x + y …….(i)

log n = x - y ……..(ii)

Multiplying (i) by 2 we get,

2log m = log m² = 2x + 2y ……(iii)

Adding (ii) and (iii) we get,

⇒ log m² + log n = 2x + 2y + (x - y)

⇒ log m²n = 3x + y.

Hence, log m²n = 3x + y.

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Mathematics

Given that log m = x + y and log n = x - y, express the value of log m²n in terms of x and y.

Logarithms

Answer

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Given that log m = x + y and log n = x - y, express the value of log m2n in terms of x and y.

Logarithms

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