Question

b) (i) log2 rational or irrational? Justify your answer? (ii) log100 rational or irrational? Justify your answer ? ​

Answer 1

log 2 = 0.30102999566

Irrational

log to the base 10 2 = x

10 ^x = 2 ^1

2 cannot be expressed as 10 ^x for any value if x

hence it is Irrational

log 100 = 2

rational

let us assume that log 100 is rational

log 100 = log to the 10 100

log to the base 10 10² = 2 log to the base 10 10 = 2

now since 2 is a rational number

log 100 is also rational

thanks mark as brilliant if my answer works