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

log 23750000

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

Here, The mantissa of log 23750 is 0.3756

Let N = 23750000

Multiply and Divide N by 10⁷, we get

Thus, scientific notation 23750000 = 2.375 × 10⁷

Consider,

log 23750000 = log (2.375 × 10⁷ )

= log 2.375 + log 10⁷

(since, log (a×b) = log a + log b)

= log 2.375 + 7

(since, log 10ⁿ = n)

Thus characteristic of log 23750000 is 7

Thus, Value of log 23750000 = 7 + 0.3756 = 7.3756