Question

How i do this -> Log 5x10^-3/2x10?

Answer 1

`log(5\cdot10^(-3))/(2\cdot10)}=log\left((5)/(2)\cdot(10^(-3))/(10)\right)=log(2.5\cdot10^(-3-1)})=log(2.5\cdot10^(-4))=(*)\\\\use\ log(a\cdot b)=loga+logb\ and\ loga^b=b\cdot loga\\\\(*)=log2.5+log10^(-4)=log2.5-4log10=log2.5-4\\\vdots\\log2.5=log(25)/(10)=log25-log10=log25-1=log5^2-1=2log5-1\\\\therefore\\\\(*)=2log5-1-4=2log5-5`