What is log_{3}(40)-log_{3}(10) ?

The solution to log_{3}(40)-log_{3}(10) is 2log_{3}(2)

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simplify log_{3}(40)-log_{3}(10)

simplify

lo g_{3} (40) - lo g_{3} (10)

2 lo g_{3} (2)

Decimal Notation

1.26185 \dots

Solution steps

lo g_{3} (40) - lo g_{3} (10)

Apply log rule:

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

lo g_{3} (40) - lo g_{3} (10) = lo g_{3} (\frac{40}{10})

= lo g_{3} (\frac{40}{10})

Divide the numbers:

\frac{40}{10} = 4

= lo g_{3} (4)

Factor the number:

4 = 2^{2}

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

Apply log rule:

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

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

= 2 lo g_{3} (2)

(3^{5})^{- 2} = \frac{1}{3 ^{- 10}}

x^{2} + 3 x - 88 = 0

\frac{1}{3} (21) - 1 - \frac{1}{2} (12)

\frac{t ^{11}}{t ^{2}}

4 x^{2} + 11 x y + 6 y^{2}

What is log_{3}(40)-log_{3}(10) ?
The solution to log_{3}(40)-log_{3}(10) is 2log_{3}(2)