log2000+2log27-log25

Question

A=2000(1+8/100)from power2 given bellow log2=0.3010,log10.8=1.0334,log2.332=03678

Answer 1

log(25)=2log(5)=2log(10/2)=2(log(10)-log(2))=2(1-0.3010)=1.398.

log(2000)=log(1000)+log(2)=3.3010.

27=3³, log(27)=3log(3), 2log(27)=6log(3).

108=2²3³; log(108)=2log(2)+3log(3); log(10.8)=log(108/10)=log(108)-1.

1.0334=log(108)-1, log(108)=2.0334.

2.0334=0.6020+3log(3),

3log(3)=1.4314, log(3)=0.4771; 6log(3)=2log(27)=2.8626.

log(2000)+2log(27)-log(25)=

3.3010+2.8626-1.398=4.7656.