What is 2log_{3}(x)+log_{3}(x-3) ?

The solution to 2log_{3}(x)+log_{3}(x-3) is log_{3}(x^2(x-3))

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simplify 2log_{3}(x)+log_{3}(x-3)

simplify

2 lo g_{3} (x) + lo g_{3} (x - 3)

lo g_{3} (x^{2} (x - 3))

Solution steps

2 lo g_{3} (x) + lo g_{3} (x - 3)

Apply log rule:

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

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

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

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

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

lo g_{10} (2) + lo g_{10} (18)

lo g_{10} (y^{8} z)

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

lo g_{10} (3 x + 1) - lo g_{10} (3 x^{2} - 5 x - 2)

ln (2 e^{1})

What is 2log_{3}(x)+log_{3}(x-3) ?
The solution to 2log_{3}(x)+log_{3}(x-3) is log_{3}(x^2(x-3))