If log 2 x = a and log 3 y = a, write 72 a in terms of x and y.

Given, ⇒ log 2 x = a ⇒ x = 2 a ........(1) ⇒ log 3 y = a ⇒ y = 3 a ........(2) Simplifying (72) a , we get : ⇒ 72 a ⇒ (2 3 × 3 2 ) a ⇒ (2 3 ) a × (3 2 ) a ⇒ (2 a ) 3 × (3 a ) 2 Substituting value of 2 a and 3 a from equation (1) and (2), in above equation, we get : ⇒ x 3 .y 2 Hence, 72 a = x 3 .y 2

Mathematics

If log₂ x = a and log₃ y = a, write 72^a in terms of x and y.

Logarithms

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Answer

Given,

⇒ log₂ x = a

⇒ x = 2^a ……..(1)

⇒ log₃ y = a

⇒ y = 3^a ……..(2)

Simplifying (72)^a, we get :

⇒ 72^a

⇒ (2³ × 3²)^a

⇒ (2³)^a × (3²)^a

⇒ (2^a)³ × (3^a)²

Substituting value of 2^a and 3^a from equation (1) and (2), in above equation, we get :

⇒ x³.y²

Hence, 72^a = x³.y²

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Mathematics

If log₂ x = a and log₃ y = a, write 72^a in terms of x and y.

Logarithms

Answer

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Logarithms

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Both A and R are true and R is the incorrect reason for A.

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