What is log_{5}((12x)/(3y)) ?

The solution to log_{5}((12x)/(3y)) is 2log_{5}(2)+log_{5}(x)-log_{5}(y)

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simplify log_{5}((12x)/(3y))

simplify

lo g_{5} (\frac{12 x}{3 y})

2 lo g_{5} (2) + lo g_{5} (x) - lo g_{5} (y)

Solution steps

lo g_{5} (\frac{12 x}{3 y})

Factor the number:

12 = 3 \cdot 4

= lo g_{5} (\frac{3 \cdot 4 x}{3 y})

Cancel the common factor:

3

= lo g_{5} (\frac{4 x}{y})

Apply log rule:

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

lo g_{5} (\frac{4 x}{y}) = lo g_{5} (4 x) - lo g_{5} (y)

= lo g_{5} (4 x) - lo g_{5} (y)

Simplify

lo g_{5} (4 x) : 2 lo g_{5} (2) + lo g_{5} (x)

= 2 lo g_{5} (2) + lo g_{5} (x) - lo g_{5} (y)

lo g_{10} (16) + 2 lo g_{10} (3)

ln (\frac{10}{5})

- 4 ln (x) - 5 ln (y) - 8 ln (z)

2 ln (5) - ln (4)

ln (\frac{x}{x ^{2} + 9})

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