What is log_{9}(18)+log_{9}(2) ?

The solution to log_{9}(18)+log_{9}(2) is log_{3}(6)

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simplify log_{9}(18)+log_{9}(2)

simplify

lo g_{9} (18) + lo g_{9} (2)

lo g_{3} (6)

Decimal Notation

1.63092 \dots

Solution steps

lo g_{9} (18) + lo g_{9} (2)

Apply log rule:

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

lo g_{9} (18) + lo g_{9} (2) = lo g_{9} (18 \cdot 2)

= lo g_{9} (18 \cdot 2)

Multiply the numbers:

18 \cdot 2 = 36

= lo g_{9} (36)

Factor the number:

36 = 6^{2}

= lo g_{9} (6^{2})

Apply log rule:

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

lo g_{9} (6^{2}) = 2 lo g_{9} (6)

= 2 lo g_{9} (6)

Factor the number:

9 = 3^{2}

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

Apply log rule:

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

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

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

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

= lo g_{3} (6)

ln (z) + ln (12 x)

ln (\frac{e x ^{6}}{y})

2 lo g_{2} (x) + 4 lo g_{2} (y)

(lo g_{10} (6) + lo g_{10} (4)) - lo g_{10} (3)

2 lo g_{10} (5) - 6 lo g_{10} (3)

What is log_{9}(18)+log_{9}(2) ?
The solution to log_{9}(18)+log_{9}(2) is log_{3}(6)