Subject: characteristics of logs

Name: andrew strauss
Who is asking: Student
Level: Secondary

Question:
What is the characteristic of log base 18 of 1980 ?

The characteristic of a logarithm is the integral part of the logarithm. The mantissa is the decimal part. So, for example

and thus the characteristic is 4 and the mantissa 0.94694.

Calculating the mantissa usually involves a calculator or computer but calculating the characteristic can be straightforward. In the problem above suppose that

then, but the definition of the logarithm function

But

Thus y is between 4 and 5 and hence the characteristic of log₈(29345) is 4.