If log2 y = x and log3 z = x, find 72x in terms of y and z.

Given: log2 y = x and log3 z = x ⇒ y = 2x and z = 3x Now, 72x = (23. 32)x = 23x. 32x = (2x)3. (3x)2 = (y)3. (z)2 = y3.z2 Hence, 72x = y3z2.

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Mathematics

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Given: log₂ y = x and log₃ z = x

⇒ y = 2^x and z = 3^x

Now, 72^x = (2³. 3²)^x

= 2^3x. 3^2x

= (2^x)³. (3^x)²

= (y)³. (z)²

= y³.z²

Hence, 72^x = y³z².

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