Question

is log5base 10 rational or irrational?​

Answer 1

$\log_{10}5$ is an irrational number.

Step-by-step explanation:

In the question

The given expression is:

$\log_{10}5$

We know that,

Rational number can be written in form of $\frac{p}{q}$. Where p and q are integers and q is non-zero.

Irrational number can not be written in form of $\frac{p}{q}$.

Now, apply logarithmic property

$\log_{a}x = y$

=> $a^{y} = x$

$\log_{10}5 = y$

=> $10^{y} = 5$

$10^{y}$ can not be written as 5.

So, $\log_{10}5$ is not a ration number.

Thus, $\log_{10}5$ is an irrational number.