Question

If ${log}_{10}2=0.3010$ and ${log}_{10}3=0.4771$ Find value of ${log}_{10}540=$

Answer 1

We know that $540=27\times 2\times 10$

${\log }_{10}540={\log }_{10}(27\times 2\times 10)$

$={\log }_{10}27+{\log }_{10}2+{\log }_{10}10$

$={\log }_{10}{3}^3+{\log }_{10}2+{\log }_{10}10$

$=3{\log }_{10}3+{\log }_{10}2+{\log }_{10}10$

$=3\times 0.4771+0.3010+1$

$=1.4313‬+1.3010=2.7323‬$