What is log_{10}(0.1)-log_{10}(0.001) ?

The solution to log_{10}(0.1)-log_{10}(0.001) is 2

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simplify log_{10}(0.1)-log_{10}(0.001)

simplify

lo g_{10} (0.1) - lo g_{10} (0.001)

2

Solution steps

lo g_{10} (0.1) - lo g_{10} (0.001)

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{10} (0.1) - lo g_{10} (0.001) = lo g_{10} (\frac{0.1}{0.001})

= lo g_{10} (\frac{0.1}{0.001})

\frac{0.1}{0.001} = 100

= lo g_{10} (100)

Factor the number:

100 = 1 0^{2}

= lo g_{10} (1 0^{2})

Apply log rule:

lo g_{a} (a^{b}) = b

= 2

ln (16) - ln (3)

ln (8) + \frac{1}{2} ln (x + 3) - 3 ln (1 + x)

lo g_{b} (x y)

(- 1.679) + (2477.572) ln (\frac{0.5}{1.5})

lo g_{10} (\frac{a ^{2}}{b c ^{3}})

What is log_{10}(0.1)-log_{10}(0.001) ?
The solution to log_{10}(0.1)-log_{10}(0.001) is 2