Question

is log 3 rational or irrational​

Answer 1

Heya friend,

Here is your answer.. :)

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Answer:

      Log 3 is irrational

Step-by-step explanation:

Let us assume that log(3) is rational and make it lead to a contradiction.

If log(3) is rational, we can write this as:

log(3) = x/y where x and y are integers.

This means:

3 = 10^(x/y)

==> 3^y = 10^x

Since 3 raised to any integer power is odd and 10 raised to any integer power is even and that a number cannot be both even and odd, this cannot be true! Hence, we have reached at a contradiction and so log(3) must be irrational.

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Hope this will help you..

Be Brainly.. :)

Answer 2

Hey mate❤❤

The log (base 10) of any number that is not 10 to some rational power is going to be irrational. However, 10 to a rational, but non-integer, power will itself be irrational.

So even though 10^.5 is irrational, the log of it is rational.

Although 8 is rational, its log would be irrational because it is 10 to some irrational power.

100 is rational and its log is also rational

Pi is irrational, and so is its log.

If the log is some other base, substitute 10 for that base. For example, in some countries, log is base e (what Americans would call natural log (ln))

Hope this will helpful for you❤❤