Question

怎么笔算log以10为底2的对数

Answer 1

精确到两位小数：
lg2=0.1lg2^10=0.1lg1024=0.1lg(1000×1.024)
=0.3+0.1lg1.024=0.3+0.01lg1.024^10
=0.3+0.01lg1.2xx=0.30
精确到3位小数：
lg2=0.1lg2^10=0.1lg1024=0.1lg(1000×1.024)
=0.3+0.1lg1.024=0.3+0.001lg1.024^100
=0.3+0.001lg10.xx
=0.3+0.001lg(10×1.0xx)
=0.3+0.001+0.001lg1.0xx
=0.301
其中
1.024^100=1+100×0.024^1+100×99/2×0.024^2+100×99×98/（1×2×3）×0.024^3+
……+100！/(100-n)！/n！×0.024^n+0.024^100=10.71x
x为0至9不等的数字

Answer 2

lg2
=0+0.1lg2^10
=0+0.1lg1024=0.1lg(1000×24)=0.3+0.1lg24=0.3+0.01lg24^10
=0.3+0.01lg1.0^10
=0.3+0.01lg1.0
=0.30