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'?
- A40 dB
- B100 dB
- C20 dB
- D200 dB
Show answer & explanationAnswer & 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.