What is 2log_{10}(x-3)-3log_{10}(x) ?

The solution to 2log_{10}(x-3)-3log_{10}(x) is log_{10}(((x-3)^2)/(x^3))

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simplify 2log_{10}(x-3)-3log_{10}(x)

simplify

2 lo g_{10} (x - 3) - 3 lo g_{10} (x)

lo g_{10} (\frac{( x - 3 ) ^{2}}{x ^{3}})

Solution steps

2 lo g_{10} (x - 3) - 3 lo g_{10} (x)

Apply log rule:

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

2 lo g_{10} (x - 3) = lo g_{10} ((x - 3)^{2})

= lo g_{10} ((x - 3)^{2}) - 3 lo g_{10} (x)

Apply log rule:

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

3 lo g_{10} (x) = lo g_{10} (x^{3})

= lo g_{10} ((x - 3)^{2}) - lo g_{10} (x^{3})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{10} ((x - 3)^{2}) - lo g_{10} (x^{3}) = lo g_{10} (\frac{( x - 3 ) ^{2}}{x ^{3}})

= lo g_{10} (\frac{( x - 3 ) ^{2}}{x ^{3}})

ln (\frac{20 - 7 \cdot 0.0679}{40 - 7 \cdot 0.0679})

lo g_{x} (\frac{1}{3 x})

ln (\frac{3 x ^{2}}{θ} \cdot e^{- \frac{3 x ^{2}}{θ}})

ln (x^{2} - 2 x - 24) - ln (x + 4)

- lo g_{10} (4 \cdot 1 0^{- 6})

What is 2log_{10}(x-3)-3log_{10}(x) ?
The solution to 2log_{10}(x-3)-3log_{10}(x) is log_{10}(((x-3)^2)/(x^3))