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

log 23750

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

Here, The mantissa of log 23750 is 0.3756

Let N = 23750

Multiply and Divide N by 10000, we get

Thus, scientific notation of 23750 = 2.3750 × 10⁴

Consider,

log 23750 = log (2.3750 × 10⁴ )

= log 2.375 + log 10⁴

(since, log (a×b) = log a + log b)

= log 2.375 + 4

(since, log 10ⁿ = n)

Thus characteristic of log 23750 is 4

Thus, Value of log 23750 = 4 + 0.3756 = 4.3756