CMA Foundation · Fundamentals of Business Mathematics and Statistics · Indices and Logarithms
Given log10(2) = 0.3010 and log10(3) = 0.4771, how many digits are there in the integral part of 6^20?
6^20 has 16 digits. Since log 6 = 0.7781, log 6^20 = 20 × 0.7781 = 15.562. The characteristic is 15, and the number of digits is the characteristic plus one, giving 16.
- A15
- B16Correct
- C17
- D14
Explanation
log 6 = 0.3010 + 0.4771 = 0.7781. Then log 6^20 = 20 × 0.7781 = 15.562. The characteristic is 15, so the number has 15 + 1 = 16 digits. Option 15 forgets to add 1 to the characteristic.
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