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

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

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

simplify

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

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

Solution steps

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

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:

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

Apply log rule:

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

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

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

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

ln (\frac{r ^{3} t ^{4}}{s ^{6}})

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

- lo g_{10} (3.5 \cdot 1 0^{- 11})

4 ln ∣ x ∣ + 4 ln ∣ x + 1 ∣ + C

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