The mantissa of log 23750 is 0.3756. Find the value of the following.

log 0.2375

Mantissa: Every logarithm consist of a fractional part called the mantissa.

Here, The mantissa of log 23750 is 0.3756

Let N = 0.2375

Divide N by 10000 to remove decimal, we get

Multiply and Divide N by 1000, we get

Thus, scientific notation 0.2375 = 2.375 × 10^–1

Consider,

log 0.2375 = log (2.375 × 10^–1 )

= log 2.375 + log 10^–1

(since, log (a×b) = log a + log b)

= log 2.375 + (–1)

(since, log 10ⁿ = n)

Thus characteristic of log 0.2375 is –1

Thus, Value of log 0.2375 = –1 + 0.3756 = ̅1.3756