What is log_{3}((3a)/(bc)) ?

The solution to log_{3}((3a)/(bc)) is 1+log_{3}(a)-log_{3}(b)-log_{3}(c)

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simplify log_{3}((3a)/(bc))

simplify

lo g_{3} (\frac{3 a}{b c})

1 + lo g_{3} (a) - lo g_{3} (b) - lo g_{3} (c)

Solution steps

lo g_{3} (\frac{3 a}{b c})

Apply log rule:

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

lo g_{3} (\frac{3 a}{b c}) = lo g_{3} (3 a) - lo g_{3} (b c)

= lo g_{3} (3 a) - lo g_{3} (b c)

lo g_{3} (3 a) = 1 + lo g_{3} (a)

lo g_{3} (b c) = lo g_{3} (b) + lo g_{3} (c)

= 1 + lo g_{3} (a) - (lo g_{3} (b) + lo g_{3} (c))

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{3} (b) + lo g_{3} (c)) = - lo g_{3} (b) - lo g_{3} (c)

= 1 + lo g_{3} (a) - lo g_{3} (b) - lo g_{3} (c)

5 ln (x) + \frac{1}{2} ln (y)

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

- lo g_{10} (4.73 \cdot 1 0^{- 9})

lo g_{3} (\frac{x ^{3}}{x + 2})

lo g_{2} (\frac{y}{15})

What is log_{3}((3a)/(bc)) ?
The solution to log_{3}((3a)/(bc)) is 1+log_{3}(a)-log_{3}(b)-log_{3}(c)