If log 37.5 = 1.574, then number of digits in (375) ^10 =?     [log base = 10]

To find the number of digits in (375)^10, we can use the formula:

Number of digits in N = log10(N) + 1

First, we need to find the value of log10(375^10).

We know that log(a^b) = b * log(a).

So, log10(375^10) = 10 * log10(375)

We are given that log10(37.5) = 1.574.

We can express 375 as 37.5 * 10, so log10(375) = log10(37.5) + log10(10) = 1.574 + 1 = 2.574.

Therefore, log10(375^10) = 10 * 2.574 = 25.74.

Finally, the number of digits in (375)^10 = log10(375^10) + 1 = 25.74 + 1 = 26.74.

Since the number of digits must be an integer, we round up to the nearest whole number.

So, the number of digits in (375)^10 is 27.