What is log_{5}(12)-log_{5}(3) ?

The solution to log_{5}(12)-log_{5}(3) is 2log_{5}(2)

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simplify log_{5}(12)-log_{5}(3)

simplify

lo g_{5} (12) - lo g_{5} (3)

2 lo g_{5} (2)

Decimal Notation

0.86135 \dots

Solution steps

lo g_{5} (12) - lo g_{5} (3)

Apply log rule:

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

lo g_{5} (12) - lo g_{5} (3) = lo g_{5} (\frac{12}{3})

= lo g_{5} (\frac{12}{3})

Divide the numbers:

\frac{12}{3} = 4

= lo g_{5} (4)

Factor the number:

4 = 2^{2}

= lo g_{5} (2^{2})

Apply log rule:

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

lo g_{5} (2^{2}) = 2 lo g_{5} (2)

= 2 lo g_{5} (2)

ln (3 x) - ln (x)

ln (x e^{(7 x)})

lo g_{10} (20) + lo g_{10} (\frac{1}{10})

\frac{5}{6} lo g_{2} (\frac{5}{6}) + \frac{1}{6} lo g_{2} (\frac{1}{6})

6 lo g_{2} (u) + 3 lo g_{2} (v)

What is log_{5}(12)-log_{5}(3) ?
The solution to log_{5}(12)-log_{5}(3) is 2log_{5}(2)