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

log 0.00002375

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

Here, The mantissa of log 23750 is 0.3756

Let N = 0.00002375

Divide N by 10⁸ to remove decimal, we get

Multiply and Divide N by 1000, we get

Thus, scientific notation 0.00002375 = 2.375 × 10^–5

Consider,

log 0.00002375 = log (2.375 × 10^–5 )

= log 2.375 + log 10^–5

(since, log (a×b) = log a + log b)

= log 2.375 + (–5)

(since, log 10ⁿ = n)

Thus characteristic of log 0.00002375 is –5

Thus, Value of log 0.00002375 = –5 + 0.3756 = ̅5.3756