Question

Please help me to do tis problem please​

Answer 1

Answer:

let us assume that log2 is rational

log2= p/q where p and q are integers

since log1=0 and log10=1

0<log2<1

and therefore p<q

now 2 = 10 power p/q

2 power q - p =5 power

p-q is an integer greater then 0

lhs is even rhs is odd

which contradicts the fact

hence log 2 with base 10 is irrational

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