Question

If log2=0.3010 and log 3=0.4771,then the value of log 144 is

Answer 1

log 144

=> log ( 2 *72 )

=> log ( 2²*2²*3²)

=> log(2^4*3^2)

=> log2^4+log3^2

=> 4(log2)+2(log3)

=> 4(0.3010)+2(0.4771)

=>1.2040+0.9542

=> 2.1582

Answer 2

log144 = log(2 × 2 × 2 × 2 × 3 × 3 )
= log(2⁴ × 3²)
= log(2⁴) + log(3²)

use the concept,
Loga^n = nloga

= 4log(2) + 2log(3)
now, put, log2 = 0.3010 and log3 = 0.4771

= 4 × 0.3010 + 2 × 0.4771
= 2{2 × 0.301 + 0.4771 }
= 2{ 0.602 + 0.4771}
= 2 × 1.0791
= 2.1582