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

log 23.75

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

Here, The mantissa of log 23750 is 0.3756

Let N = 23.75

Divide N by 100 to remove decimal, we get

Multiply and Divide N by 1000, we get

Thus, scientific notation 23.75 = 2.375 × 10¹

Consider,

log 23.75 = log (2.375 × 10¹ )

= log 2.375 + log 10¹

(since, log (a×b) = log a + log b)

= log 2.375 + 1

(since, log 10ⁿ = n)

Thus characteristic of log 23.75 is 1

Thus, Value of log 23.75 = 1 + 0.3756 = 1.3756