if log 2 0 30103 and log 3 0 4771 find the number of digits in 648 5 ........

Quantitative Aptitude (CDS) Logarithm

Download Solution PDF

if log 2 = 0.30103 and log 3 = 0.4771, find the number of digits in (648)⁵.

छोटे Courses बड़े Results

Master Logarithm

Prepare through Micro-courses

Try Now

Explanation:

log(648)⁵
= 5 log(648)
= 5 log(81 × 8)
= 5[log(81) + log(8)]
=5 [log(3⁴) + log(2³)]
=5[4log(3) + 3log(2)]
= 5[4 × 0.4771 + 3 × 0.30103]
= 5(1.9084 + 0.90309)
= 5 × 2.81149
≈ 14.05
ie, log(648)⁵ ≈ 14.05
ie, its characteristic = 14
Hence, number of digits in (648)⁵ = 14+1 = 15