ASVAB (Armed Services Vocational Aptitude Battery)Mathematics Knowledge (MK)Hard

A team of engineers is testing a new antenna. The signal strength 'S' in decibels is given by the formula S = 20 log(P), where 'P' is the power ratio. If the power ratio 'P' is 100, what is the signal strength 'S'?

  1. A40 dB
  2. B100 dB
  3. C20 dB
  4. D200 dB
Show answer & explanation

Correct answer: A. 40 dB

Substitute P=100 into the formula: S = 20 log(100). The logarithm of 100 base 10 is 2 (since 10^2 = 100). So, S = 20 * 2 = 40 dB.

Why the other options are wrong

  • B. This is the value of P, not S.
  • C. This would be if log(100) was 1, or if P was 10.
  • D. This would be if log(100) was 10, or if P was 10,000,000,000.

Logarithm Evaluation

Determining the exponent to which a base must be raised to produce a given number.

  • log_b(x) = y means b^y = x.
  • Common logarithm (log) implies base 10.
  • Used in decibels, pH scale, earthquake magnitudes.

Memory trick: Logs are like Ladders to Exponents.

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