How do you simplify ${log}_{10} (\frac{1}{100}) - {log}_{10} (\frac{1}{1000})$ $Log_10 (1/100) - log_10 (1/1000)$ ?

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Answer 1 · 2018-04-30T08:38:38

$1$ $1$

We know that,

$(1) \frac{1}{a^{n}} = a^{- n}$ $color(red)((1)1/(a^n)=a^(-n)$

$(2) {log}_{a} x^{n} = n {log}_{a} x$ $color(blue)((2)log_a x^n=nlog_a x$

$(3) {log}_{a} a = 1$ $color(violet)((3)log_a a=1$

Let

$L = {log}_{10} (\frac{1}{100}) - {log}_{10} (\frac{1}{1000})$ $L=log_10(1/100)-log_10(1/1000)$

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

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

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

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

$=-2+3$

$=1$

How do you simplify Log_10 (1/100) - log_10 (1/1000) log10(1100)−log10(11000)Log_10 (1/100) - log_10 (1/1000) ?