What is 3log_{10}(x)-6log_{10}(x+1) ?

The solution to 3log_{10}(x)-6log_{10}(x+1) is log_{10}((x^3)/((x+1)^6))

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simplify 3log_{10}(x)-6log_{10}(x+1)

simplify

3 lo g_{10} (x) - 6 lo g_{10} (x + 1)

lo g_{10} (\frac{x ^{3}}{( x + 1 ) ^{6}})

Solution steps

3 lo g_{10} (x) - 6 lo g_{10} (x + 1)

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}) - 6 lo g_{10} (x + 1)

Apply log rule:

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

6 lo g_{10} (x + 1) = lo g_{10} ((x + 1)^{6})

= lo g_{10} (x^{3}) - lo g_{10} ((x + 1)^{6})

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 + 1)^{6}) = lo g_{10} (\frac{x ^{3}}{( x + 1 ) ^{6}})

= lo g_{10} (\frac{x ^{3}}{( x + 1 ) ^{6}})

ln (4) + 2 ln (x) + 3 ln (x^{2} + 3)

7 lo g_{3} (a) + 2 lo g_{3} (b) - \frac{1}{2} lo g_{3} (2 c)

lo g_{10} (a) - 2 lo g_{10} (b) + 3 lo g_{10} (c)

lo g_{10} (a) + 2 - 2 lo g_{10} (b)

4 lo g_{3} (x) + 7 lo g_{3} (y)

What is 3log_{10}(x)-6log_{10}(x+1) ?
The solution to 3log_{10}(x)-6log_{10}(x+1) is log_{10}((x^3)/((x+1)^6))