# Mistakes give rise to Problems- 13

Algebra Level 4

In maths, we do $$a\times b=ab$$. But if you do that while there is the log function, $\color{Red}{\log (a) \times \log (b) = \log (a\times b)}$ then that will be a big mistake!

But for some pairs of integers $$(a,b)$$, for which $$\log (a)$$ and $$\log (b)$$ are also integers, the above property is true. Find the sum of all $$a$$ and $$b$$ in these pairs.

If you get $$n$$ pairs $$(a_1,b_1),(a_2,b_2),\ldots,(a_n,b_n)$$, then answer should be reported as $$\displaystyle \sum_{k=1}^n \biggl(a_k+b_k \biggr)$$

Details and assumptions:

• Assume we take the log in base 10.

• We only consider $$a$$ and $$b$$ asintegers, and so are $$\log(a)$$ and $$\log(b)$$

###### This problem is a part of the set Mistakes Give rise to problems.
×

Problem Loading...

Note Loading...

Set Loading...