Zadanie 2
log5\approx0,7.
a)
log 50=log(5*10)=log5+log10\approx0,7+1\approx1,7
b)
log 500=log(5*100)=log5+log100\approx0,7+log10^2\approx0,7+2\approx2,7
c)
log 0,05=log(5*0,01)=log5+log\frac{1}{100}\approx0,7+log100^{-1}\approx0,7+log(10^2)^{-1}\approx
\approx 0,7+log10^{-2}\approx0,7+(-2)\approx-1,3
d)
log \frac{1}{5}=log(5*\frac{1}{10})=log5+log\frac{1}{10}\approx0,7+log10^{-1}\approx0,7+(-1)\approx-0,3
Zadanie 3
log_27\approx2,8.
a)
log_214=log_2(2*7)=log_22+log_27\approx1+2,8\approx3,8
b)
log_228=log_2(4*7)=log_24+log_27\approx log_22^2+2,8\approx2+2,8\approx4,8
c)
log_23,5=log_2(\frac{1}{2}*7)=log_2\frac{1}{2}+log_27\approx log_22^{-1}+2,8\approx-1+2,8\approx1,8
d)
log_2\frac{7}{4}= log_27-log_24\approx2,8-log_22^2\approx2,8-2\approx0,8