# How do you multiply numbers with large exponents?

May 19, 2016

See explanation. Other contributors may chose to offer other potential examples.

#### Explanation:

It all depends on the numbers.

Suppose you had ${3}^{56} \times {12}^{87}$

$\textcolor{b l u e}{\text{One possible approach could be:}}$

$\log \left({3}^{56}\right) + \log \left({12}^{87}\right) \text{ "->" } \left[56 \times \log \left(3\right)\right] + \left[87 \times \log \left(12\right)\right]$

$\implies {3}^{56} \times {12}^{87} \text{ "->" } {\log}^{- 1} \left(\textcolor{w h i t e}{.} \left[56 \times \log \left(3\right)\right] + \left[87 \times \log \left(12\right)\right] \textcolor{w h i t e}{.}\right)$

In the 'old days' they called this the 'antilog' which is the reversing process so that you go from log back to source number