What is log_{6}(12)-log_{6}(3) ?

The solution to log_{6}(12)-log_{6}(3) is 2log_{6}(2)

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simplify log_{6}(12)-log_{6}(3)

simplify

lo g_{6} (12) - lo g_{6} (3)

2 lo g_{6} (2)

Decimal Notation

0.77370 \dots

Solution steps

lo g_{6} (12) - lo g_{6} (3)

Apply log rule:

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

lo g_{6} (12) - lo g_{6} (3) = lo g_{6} (\frac{12}{3})

= lo g_{6} (\frac{12}{3})

Divide the numbers:

\frac{12}{3} = 4

= lo g_{6} (4)

Factor the number:

4 = 2^{2}

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

Apply log rule:

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

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

= 2 lo g_{6} (2)

\frac{1}{2} lo g_{10} (x) - 2 lo g_{10} (x + 1)

\frac{1}{3} lo g_{b} (x) + 3 lo g_{b} (y) - 4 lo g_{b} (x)

ln (4) + \frac{1}{3} ln (8)

\frac{1}{2} lo g_{10} (c) + 3 lo g_{10} (d)

- \frac{5}{7} lo g_{2} (\frac{5}{7}) - \frac{2}{7} lo g_{2} (\frac{2}{7})

What is log_{6}(12)-log_{6}(3) ?
The solution to log_{6}(12)-log_{6}(3) is 2log_{6}(2)