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Popular >

simplify 3log_{3}(2)-log_{3}(72)

Solution

simplify

3 lo g_{3} (2) - lo g_{3} (72)

Solution

- 2

Solution steps

3 lo g_{3} (2) - lo g_{3} (72)

Apply log rule:

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

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

= lo g_{3} (2^{3}) - lo g_{3} (72)

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{3} (2^{3}) - lo g_{3} (72) = lo g_{3} (\frac{2 ^{3}}{72})

= lo g_{3} (\frac{2 ^{3}}{72})

\frac{2 ^{3}}{72} = 3^{- 2}

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

Apply log rule:

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

= - 2

Popular Examples

simplify 1/5-2/3+1 simplify

\frac{1}{5} - \frac{2}{3} + 1

2 x < 0

simplify (-5x)^{-2}simplify

(- 5 x)^{- 2}

55<5x-5((x-11)/2)<= 110

55 < 5 x - 5 (\frac{x - 11}{2}) \leq 110

(x+1)^2-3x*(x+2)=3

(x + 1)^{2} - 3 x \cdot (x + 2) = 3

Frequently Asked Questions (FAQ)

What is 3log_{3}(2)-log_{3}(72) ?
The solution to 3log_{3}(2)-log_{3}(72) is -2