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{3 x ^{5}}{y})

- lo g_{10} (5.8 \cdot 1 0^{- 3})

ln (9) + \frac{1}{2} ln (x + 4) - 2 ln (1 + x)

ln^{3} (2 x)

ln (\frac{58.5}{69800})

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))