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What will be the value of integer z if (log2z)2 – log2z4 – 32 = 0?

What will be the value of integer z if (log2z)2 – log2z4 – 32 = 0? Correct Answer 256

Given, (log2z)2 – log2z4 – 32 = 0 ➩ (log2z)2 – 4log2z – 32 = 0 Let log2z = a ➩ a2 – 4a – 32 = 0 ➩ a2 – 8a + 4a – 32 = 0 ➩ a(a – 8) + 4(a – 8) = 0 ➩ (a – 8) (a + 4) = 0 ➩ a = 8, – 4 ➩ log2z = 8 or log2z = – 4 ➩ z = 28 = 256 or z = 2-4 = 1 / 16 Since z is an integer therefore z = 256.

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