High School Mathematics 3.7 Finding Number of Digits

If the characteristic of the logarithm is n, the number will have 'n+1' digits.

Example:
log_{10} 2 = 0.3010, find the number of digits in 16^{20}. Solution:
Let x = 16^{20}
Take logarithm on both sides,
log x = log 16^{20}
= 20 log 16
= 20 log 2^{4}
= 20 * 4 log 2
= 80 * 0.3010
= 24.08
The characteristic is 24,
So the number of digits in 16^{20} is 24 + 1 = 25.

Directions: Solve the following problems. Also write at least ten examples of your own.