Logarithm-8

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How many zeros are there between the decimal point and the first significant digit in (i) 2-30 (ii) 4-16

Solution: (i) Let x = 2-30

Therefore, log x = log 2-30 = - 30 log 2 = - 30 (0.3010)

= - 9.0300

= ‾10.9700

Therefore, the number of zeros between the decimal place and the significant digit = 9

(ii) Let x = 4-16

log x = log 4-16 = - 16 log 4 = -16 (0.6020)

= - 9.6320 = ‾10.3680

Therefore, the number of zeros between the decimal place and the significant digit = 9

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