What is 3log_{4}(x+1)-log_{4}(x) ?

The solution to 3log_{4}(x+1)-log_{4}(x) is log_{4}(((x+1)^3)/x)

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simplify 3log_{4}(x+1)-log_{4}(x)

simplify

3 lo g_{4} (x + 1) - lo g_{4} (x)

lo g_{4} (\frac{( x + 1 ) ^{3}}{x})

Solution steps

3 lo g_{4} (x + 1) - lo g_{4} (x)

Apply log rule:

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

3 lo g_{4} (x + 1) = lo g_{4} ((x + 1)^{3})

= lo g_{4} ((x + 1)^{3}) - lo g_{4} (x)

Apply log rule:

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

lo g_{4} ((x + 1)^{3}) - lo g_{4} (x) = lo g_{4} (\frac{( x + 1 ) ^{3}}{x})

= lo g_{4} (\frac{( x + 1 ) ^{3}}{x})

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

ln (\frac{a}{b}) - 2 ln (a^{3}) + 4 ln (b)

\frac{π}{8} ln (2)

lo g_{2} (5) + lo g_{2} (12) - lo g_{2} (3.75)

ln (x^{4} e^{2 x})

What is 3log_{4}(x+1)-log_{4}(x) ?
The solution to 3log_{4}(x+1)-log_{4}(x) is log_{4}(((x+1)^3)/x)