What is simplify-6log_{3}(x+1)+4log_{3}(2x) ?

The solution to simplify-6log_{3}(x+1)+4log_{3}(2x) is log_{3}((16x^4)/((x+1)^6))

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simplify-6log_{3}(x+1)+4log_{3}(2x)

simplify

- 6 lo g_{3} (x + 1) + 4 lo g_{3} (2 x)

lo g_{3} (\frac{16 x ^{4}}{( x + 1 ) ^{6}})

Solution steps

- 6 lo g_{3} (x + 1) + 4 lo g_{3} (2 x)

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

4 lo g_{3} (2 x) = lo g_{3} ((2 x)^{4})

= - lo g_{3} ((x + 1)^{6}) + lo g_{3} ((2 x)^{4})

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{3} ((2 x)^{4}) - lo g_{3} ((x + 1)^{6}) = lo g_{3} (\frac{( 2 x ) ^{4}}{( x + 1 ) ^{6}})

= lo g_{3} (\frac{( 2 x ) ^{4}}{( x + 1 ) ^{6}})

Simplify

(2 x)^{4} : 16 x^{4}

= lo g_{3} (\frac{16 x ^{4}}{( x + 1 ) ^{6}})

ln (3) + ln (6) - ln (9)

ln (\frac{( x + 1 )}{x - 1})

- lo g_{10} (1.26 \cdot 1 0^{- 6})

4 ln (3 x^{2}) - \frac{1}{2} ln (9 x^{8})

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

What is simplify-6log_{3}(x+1)+4log_{3}(2x) ?
The solution to simplify-6log_{3}(x+1)+4log_{3}(2x) is log_{3}((16x^4)/((x+1)^6))