What is 6log_{10}(x)-8log_{10}(x+1) ?

The solution to 6log_{10}(x)-8log_{10}(x+1) is log_{10}((x^6)/((x+1)^8))

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simplify 6log_{10}(x)-8log_{10}(x+1)

simplify

6 lo g_{10} (x) - 8 lo g_{10} (x + 1)

lo g_{10} (\frac{x ^{6}}{( x + 1 ) ^{8}})

Solution steps

6 lo g_{10} (x) - 8 lo g_{10} (x + 1)

Apply log rule:

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

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

= lo g_{10} (x^{6}) - 8 lo g_{10} (x + 1)

Apply log rule:

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

8 lo g_{10} (x + 1) = lo g_{10} ((x + 1)^{8})

= lo g_{10} (x^{6}) - lo g_{10} ((x + 1)^{8})

Apply log rule:

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

lo g_{10} (x^{6}) - lo g_{10} ((x + 1)^{8}) = lo g_{10} (\frac{x ^{6}}{( x + 1 ) ^{8}})

= lo g_{10} (\frac{x ^{6}}{( x + 1 ) ^{8}})

lo g_{10} (x^{2} - 4) - lo g_{10} (x - 2)

ln (\frac{( x + 3 )}{x y})

\frac{1}{4} + ln (\frac{π}{3})

lo g_{8} (11 x)

lo g_{3} (\frac{81 x}{x ^{2} + 9})

What is 6log_{10}(x)-8log_{10}(x+1) ?
The solution to 6log_{10}(x)-8log_{10}(x+1) is log_{10}((x^6)/((x+1)^8))