- All numbers lying between 1 and 0.1 have logarithms lying between 0 and -1. Since decimal part is always written positive, the characteristic is -1.
- All numbers lying between 0.1 and 0.01 have their logarithms lying between -1 and -2 as the characteristic of their logarithms.
Note: In general, the logarithm of a number having n zeros just after the decimal point is (n + 1) + a fraction.
We will try to convert the decimal part into a positive quantity. Adding and subtracting 2 to -1.602, we get
log(0.025) = -1.602 + 2 - 2 = (2 - 1.602) - 2 = -2 + 0.398
Note: Remember that logarithms and indices are transformation of one another.
- In indices, we learnt that any number raised to 0 is 1,
- We also know that any number raised to unity is itself,