[Solved]: If $log xy=log x+log y$ then why multiplication is harder than addition?

If $log xy = log x + log y$ then why is multiplication harder than addition?

That’s not a fair comparison: you’re not comparing like with like. If you, instead, phrase it as “If $xy = exp(log x + log y)$ then why is multiplication harder than addition?” then the answer is obvious. Multiplication, done that way, is harder than addition because doing addition just involves doing addition, whereas multiplication involves doing addition, taking logs twice and exponentiating.

How can we calculate the $log x$ and $exp x$ functions in a computer?

The main methods are to either use something like a Taylor series or table look-up and interpolation. Taylor series express functions as sums, e.g., $exp x = sum_{i=0}^{infty} x^i/i!$. Add up as many terms as you need to get the desired level of accuracy – note that this involves many additions and many multiplications. Table look-up and interpolation is essentially the same way that paper log tables work. To calculate, say, $log 4.3$, you’d look up $log 4$ and $log 5$ and approximate $log 4.3$ as being three-tenths of the way between them. (In reality, the table would have more decimal places.) This involves a few additions and multiplications, and a lot of memory.