Question

is log10 5 rational number or irrational number? justify your answer. ​

Answer 1

log10 5 is an irrational number.

justification : let log10 5 is a rational number then it is in the form of P/Q , where P and Q are positive integers.

i.e., log10 5 = P/Q

⇒Qlog10 5 = P

⇒log10 5^Q = P

⇒ 5^Q = 10^P

⇒5^Q = 2^P × 5^P

⇒5^(Q - P) = 2^P

we know, 5 and 2 are prime numbers. so there is no integer multiple of 5 equal to 3 and vice - versa. so our assumption is wrong.

therefore, log10 5 is not a rational number.it is an irrational number.

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If log10 2 = 0.3010; log10 3 = 0.4771 and log10 7 = 0.8451 then find log10 105?

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Answer 2

Answer:

1245556788990098777655