Question

if log5=0.6990 then number of digits 5⁷ is ________??​

Answer 1

Number of digits in any number n is:

$\lceil \sf log_{10}(n) \rceil$

• where, ⌈ . ⌉ is the ceiling function

Therefore, the number of digits in 5⁷ is

$\lceil \sf log_{10}( {5}^{7} ) \rceil = \lceil 7\sf log_{10}(5) \rceil$

$\lceil7 log_{10}(5) \rceil = \lceil7 \times 0.699 \rceil$

$\lceil4.893 \rceil = 5$

Therefore, there are 5 digits in the number 5⁷.