If log (0.57) = 1756, then the value of log 57 + log (0.57)3

If log (0.57) = 1756, then the value of log 57 + log (0.57)³ + log √0.57 is ?

1. 0.902
2. 1.902
3. 1.146
4. 2.146

Correct Option: A

Given Exp.
= log (57 x 100 / 100) + 3log(0.57) + 1/2log(0.57)
= log (0.57) + log 10² + 3log(0.57) +1/2log (0.57)
= (1 + 3 + 1/2) log(0.57) + 2 [∵ log10² = 2]
= (4.5 x 1.756) + 2 = 4.5 x (-1 + 0.756) + 2
= 3.402 - 4.5 + 2
= 0.902

Logarithm

Aptitude

Correct Option: A