How do you simplify #Log_10 (1/100) - log_10 (1/1000) #?

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Answer 1 · 2018-04-30T08:38:38

#1#

We know that,

#color(red)((1)1/(a^n)=a^(-n)#

#color(blue)((2)log_a x^n=nlog_a x#

#color(violet)((3)log_a a=1#

Let

#L=log_10(1/100)-log_10(1/1000)#

#=log_10color(red)((1/(10^2)))-log_10 color(red)((1/(10^3))...toApply(1))#

#=log_10(10^color(blue)((-2)))-log_10(10^color(blue)((-3)))...tocolor(blue)(Apply(2))#

#=color(blue)(-2)log_10 10-color(blue)((-3))log_10 10#

#=-2color(violet)((1))+3(color(violet)(1))...tocolor(violet)(Apply(3)#

#=-2+3#

#=1#