Q. Which of the following is true for log_a(b) and log_a(c) if b < c? (2019)
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A.
log_a(b) < log_a(c)
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B.
log_a(b) > log_a(c)
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C.
log_a(b) = log_a(c)
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D.
None of the above
Solution
If a > 1, then log_a(b) < log_a(c) when b < c.
Correct Answer:
A
— log_a(b) < log_a(c)
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Q. Which of the following is true for log_a(bc)?
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A.
log_a(b) + log_a(c)
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B.
log_a(b) - log_a(c)
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C.
log_a(bc) = log_a(b) * log_a(c)
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D.
None of the above
Solution
log_a(bc) = log_a(b) + log_a(c) by the product rule of logarithms.
Correct Answer:
A
— log_a(b) + log_a(c)
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Q. Which of the following numbers is a perfect square?
Solution
25 is a perfect square (5^2).
Correct Answer:
C
— 25
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Q. Which of the following represents the complex number 4 in polar form?
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A.
4(cos 0 + i sin 0)
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B.
4(cos π/2 + i sin π/2)
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C.
4(cos π + i sin π)
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D.
4(cos π/4 + i sin π/4)
Solution
The polar form of a complex number r(cos θ + i sin θ) where r is the modulus and θ is the argument. Here, 4 = 4(cos 0 + i sin 0).
Correct Answer:
A
— 4(cos 0 + i sin 0)
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