What is log_{a}(x)+log_{a}(y)-log_{a}(m) ?

The solution to log_{a}(x)+log_{a}(y)-log_{a}(m) is log_{a}((xy)/m)

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simplify log_{a}(x)+log_{a}(y)-log_{a}(m)

simplify

lo g_{a} (x) + lo g_{a} (y) - lo g_{a} (m)

lo g_{a} (\frac{x y}{m})

Solution steps

lo g_{a} (x) + lo g_{a} (y) - lo g_{a} (m)

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

= lo g_{a} (x y) - lo g_{a} (m)

Apply log rule:

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

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

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

lo g_{3} (\frac{9 b ^{3} y ^{2} - 4}{y ( x + 4 ) ^{2}})

ln (9) - ln (8)

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

lo g_{4} (5 x^{2})

ln (5 \cdot x) - 1.9

What is log_{a}(x)+log_{a}(y)-log_{a}(m) ?
The solution to log_{a}(x)+log_{a}(y)-log_{a}(m) is log_{a}((xy)/m)