Question

Find the number of digits in (144)⁸⁰. If log2 = 0.3010 and log3 = 0.4771​

Answer 1

$\bold{ANSWER≈}$

I suppose the problem is finding the number of digits in 648⁵

Let x = 648⁵

Taking logarithms (to the base 10) both sides we get log x = log (648⁵) = 5 log 648 = 5 log (2³ x 3⁴) = 15 log 2 + 20 log 3 = 15 (.3010) + 20 (.4771) = 4.5150 + 9.5420 = 14.0570.

Since the logarithm of 648⁵ has 14 as the integral part, the number of digits in the number 648⁵ is 14+1 = 15.