What is log_{3}(27x^2y^5) ?

The solution to log_{3}(27x^2y^5) is 3+2log_{3}(x)+5log_{3}(y)

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simplify log_{3}(27x^2y^5)

simplify

lo g_{3} (27 x^{2} y^{5})

3 + 2 lo g_{3} (x) + 5 lo g_{3} (y)

Solution steps

lo g_{3} (27 x^{2} y^{5})

Factor the number:

27 = 3^{3}

= lo g_{3} (3^{3} x^{2} y^{5})

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{3} (3^{3} x^{2} y^{5}) = lo g_{3} (3^{3}) + lo g_{3} (x^{2} y^{5})

= lo g_{3} (3^{3}) + lo g_{3} (x^{2} y^{5})

Apply log rule:

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

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

= 3 + lo g_{3} (x^{2} y^{5})

Simplify

lo g_{3} (x^{2} y^{5}) : 2 lo g_{3} (x) + 5 lo g_{3} (y)

= 3 + (2 lo g_{3} (x) + 5 lo g_{3} (y))

Apply rule:

a + (b + c) = a + b + c

3 + (2 lo g_{3} (x) + 5 lo g_{3} (y)) = 3 + 2 lo g_{3} (x) + 5 lo g_{3} (y)

= 3 + 2 lo g_{3} (x) + 5 lo g_{3} (y)

3 x - 8 y - 2 z + 7 x + 3 y + z

\frac{x - 1}{3 x + 4} + \frac{2 x + 9}{3 x + 4}

- 144 \times - 9

10 x^{2} + 20 x

3 + \frac{1}{16}

What is log_{3}(27x^2y^5) ?
The solution to log_{3}(27x^2y^5) is 3+2log_{3}(x)+5log_{3}(y)