# Logarithm-2

### From Homeworkwiki

**Find the number of digits in 2 ^{12} x 3^{7} when written in the usual form.**

**Solution:** Let x = 2^{12} x 3^{7}

Log x = log (2^{12} x 3^{7}) = log2^{12} + log3^{7}

= 12 log 2 + 7 log 3

= 12 (0.3010) + 7(0.4771)

= 6.9517

Since, the characteristic of log x is 6, the number of digits in x i.e. 2^{12} x 3^{7} is 7