What is log_{3}(24)-log_{3}(6) ?

The solution to log_{3}(24)-log_{3}(6) is 2log_{3}(2)

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simplify log_{3}(24)-log_{3}(6)

simplify

lo g_{3} (24) - lo g_{3} (6)

2 lo g_{3} (2)

Decimal Notation

1.26185 \dots

Solution steps

lo g_{3} (24) - lo g_{3} (6)

Apply log rule:

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

lo g_{3} (24) - lo g_{3} (6) = lo g_{3} (\frac{24}{6})

= lo g_{3} (\frac{24}{6})

Divide the numbers:

\frac{24}{6} = 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)

lo g_{7} (\frac{x}{49})

lo g_{b} (\frac{x ^{3} y}{z ^{2}})

ln (\frac{x ^{2} - 1}{x ^{7}})

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

6 ln (2) - 4 ln (y)

What is log_{3}(24)-log_{3}(6) ?
The solution to log_{3}(24)-log_{3}(6) is 2log_{3}(2)