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Popular >

simplify log_{3}(6x)

Solution

simplify

lo g_{3} (6 x)

Solution

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

Solution steps

lo g_{3} (6 x)

Factor the number:

6 = 3 \cdot 2

= lo g_{3} (3 \cdot 2 x)

Apply log rule:

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

lo g_{3} (3 \cdot 2 x) = lo g_{3} (3) + lo g_{3} (2 x)

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

Apply log rule:

lo g_{a} (a) = 1

lo g_{3} (3) = 1

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

Apply log rule:

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

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

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

Apply rule:

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

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

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

Popular Examples

simplify (1/8)^{-1/3}simplify

(\frac{1}{8})^{- \frac{1}{3}}

- 45 > - 5 n

8x^2-10x-(3x^2)/7-43x=0

8 x^{2} - 10 x - \frac{3 x ^{2}}{7} - 43 x = 0

simplify (1/10)^6 simplify

(\frac{1}{10})^{6}

simplify 2/6*6/10 simplify

\frac{2}{6} \cdot \frac{6}{10}

Frequently Asked Questions (FAQ)

What is log_{3}(6x) ?
The solution to log_{3}(6x) is 1+log_{3}(2)+log_{3}(x)