if n = 10 ^ 100 and n ^ n = 10 k what is the value of k ?
"there is a simple logic to this question . ( a ^ m ) ^ n = a ^ mn so , ( 10 ^ 100 ) ^ ( 10 ^ 100 ) = 10 ^ ( 100 * ( 10 ^ 100 ) ) = 10 ^ ( ( 10 ^ 2 ) * ( 10 ^ 100 ) ) = 10 ^ ( 10 ^ 102 ) and this equals 10 ^ k so , k = 10 ^ 102 answer : c"
divide(log(10), log(power(10, 100)))