# Logarithm-8

### From Homeworkwiki

**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