Question

Evaluate
log of 4√10 base10
​

Answer 1

$1.102$

Step-by-step explanation:

$Given, \: \: log_{10}(4 \sqrt{10} ) \\ we \: \: know \: \: \boxed{ log(n.m) = log(n) + log(m) } \\ then, \: \: \: log_{10}(4 \sqrt{10} ) \\ = log_{10}(4) + log_{10}( \sqrt{10} ) \\ = log_{10}({2})^{2}+ log_{10}( {10})^{ \frac{1}{2} } \\ \: \: = 2log_{10}(2) + \frac{1}{2} log_{10}(10) \\ = 2 log_{10}(2) + \frac{1}{2} \times 1 \\ \: \: \: = 2 log_{10}(2) + \frac{1}{2} \\ \: \: \: \: \: \: \: \: = 2 \times 0.3010 + 0.5 \\ = 0.6020 + 0.5 \\ = \boxed{1.102}$