Is there a direct mathematical function/ formula for calculate this problem?
$$a^x \equiv b (\mod n)$$
$$x=\text{ind}_a b (\mod n)$$
I want to learn that;
1) What is "ind" here?
2) Is this formula enough to solve the discrete logarithm problem?
3) Is discrete logarithm a problem in mathematics?
4) Discrete logarithm only is the subject of High mathematics?
Thank you in advance for your answer.
This isn't a formula in any constructive sense. It's just the definition of the discrete logarithm, here called "$\text{ind}$" rather than "$\log$". If $x$ is the power of $a$ that results in $b$ then $x$ is the base $a$ logarithm of $b$.
So it does not tell you how to calculate the log.
The discrete logarithm problem is one of several important hard-to-calculate functions useful in computer security. If you had a quick way to find the actual values of discrete logarithms some encoded messages would be easier to break.
To understand something about this you need some elementary number theory. To dig into it you need higher mathematics (non so elementary number theory).