What is 4log_{3}(x+2)-6log_{3}(12)(x-1) ?

The solution to 4log_{3}(x+2)-6log_{3}(12)(x-1) is log_{3}(4096(x+2)^4)-6x(1+2log_{3}(2))+6

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simplify 4log_{3}(x+2)-6log_{3}(12)(x-1)

simplify

4 lo g_{3} (x + 2) - 6 lo g_{3} (12) (x - 1)

lo g_{3} (4096 (x + 2)^{4}) - 6 x (1 + 2 lo g_{3} (2)) + 6

Solution steps

4 lo g_{3} (x + 2) - 6 lo g_{3} (12) (x - 1)

lo g_{3} (12) = 1 + 2 lo g_{3} (2)

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

Expand

- 6 (1 + 2 lo g_{3} (2)) (x - 1) : - 6 x (1 + 2 lo g_{3} (2)) + 12 lo g_{3} (2) + 6

= 4 lo g_{3} (x + 2) - 6 x (1 + 2 lo g_{3} (2)) + 12 lo g_{3} (2) + 6

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

12 lo g_{3} (2) = lo g_{3} (2^{12})

= lo g_{3} ((x + 2)^{4}) - 6 x (1 + 2 lo g_{3} (2)) + lo g_{3} (2^{12}) + 6

Simplify

lo g_{3} ((x + 2)^{4}) + lo g_{3} (2^{12}) : lo g_{3} ((x + 2)^{4} \cdot 4096)

= lo g_{3} ((x + 2)^{4} \cdot 4096) - 6 x (1 + 2 lo g_{3} (2)) + 6

= lo g_{3} (4096 (x + 2)^{4}) - 6 x (1 + 2 lo g_{3} (2)) + 6

(x - 1 + 5) (x - 1 - 5)

(cos (θ) + i sin (θ))^{7}

x (x^{5} e^{5 x} + 2)

\frac{6 s ^{2} + 50}{( s + 3 ) ( s ^{2} + 4 )}

\frac{l - 12 s ^{2} - 1}{( s ^{2} + 4 ) ( s ^{2} + 1 )}

What is 4log_{3}(x+2)-6log_{3}(12)(x-1) ?
The solution to 4log_{3}(x+2)-6log_{3}(12)(x-1) is log_{3}(4096(x+2)^4)-6x(1+2log_{3}(2))+6