What is 4log_{9}(3)+2log_{9}(3) ?

The solution to 4log_{9}(3)+2log_{9}(3) is 3

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simplify 4log_{9}(3)+2log_{9}(3)

simplify

4 lo g_{9} (3) + 2 lo g_{9} (3)

3

Solution steps

4 lo g_{9} (3) + 2 lo g_{9} (3)

Add similar elements:

4 lo g_{9} (3) + 2 lo g_{9} (3) = 6 lo g_{9} (3)

= 6 lo g_{9} (3)

Factor the number:

9 = 3^{2}

= 6 lo g_{3^{2}} (3)

Apply log rule:

lo g_{a^{b}} (x) = \frac{1}{b} lo g_{a} (x), a > 0

lo g_{3^{2}} (3) = \frac{1}{2} lo g_{3} (3)

= 6 \cdot \frac{1}{2} lo g_{3} (3)

Apply log rule:

lo g_{a} (a) = 1

lo g_{3} (3) = 1

= 6 \cdot \frac{1}{2} \cdot 1

Multiply the numbers:

\frac{1}{2} \cdot 1 = \frac{1}{2}

= 6 \cdot \frac{1}{2}

6 \cdot \frac{1}{2} = 3

= 3

\frac{5 2}{3}

\frac{2 a ^{2}}{3 b} \times \frac{6 b ^{2}}{4 a}

- 4 + - 200 - 1 + - 18

(x - 3 x y) (- 5 x + 4 x y)

x^{3} - 2^{3}