Logarithm Problem

Question

How many digits does 17^100 have? = Answer

With what digit does it start? = Answer

Answer 1

let's set y = 17^100,

log(y) = log(17^100) = 100*log(17) = 123.045,

so y = 10 ^ (123.045) = 10 ^ 123 * 10 ^ 0.045 = 1.109 × 10¹²³

therefore there are 124 digits in y and it start with 1.