What is log_{10}(25x)-log_{10}(15x)+log_{10}(3y) ?

The solution to log_{10}(25x)-log_{10}(15x)+log_{10}(3y) is log_{10}(5y)

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simplify log_{10}(25x)-log_{10}(15x)+log_{10}(3y)

simplify

lo g_{10} (25 x) - lo g_{10} (15 x) + lo g_{10} (3 y)

lo g_{10} (5 y)

Solution steps

lo g_{10} (25 x) - lo g_{10} (15 x) + lo g_{10} (3 y)

Apply log rule:

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

lo g_{10} (25 x) - lo g_{10} (15 x) = lo g_{10} (\frac{25 x}{15 x})

= lo g_{10} (\frac{25 x}{15 x}) + lo g_{10} (3 y)

Apply log rule:

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

lo g_{10} (\frac{25 x}{15 x}) + lo g_{10} (3 y) = lo g_{10} (\frac{25 x}{15 x} \cdot 3 y)

= lo g_{10} (\frac{25 x}{15 x} \cdot 3 y)

Simplify

\frac{25 x}{15 x} \cdot 3 y : 5 y

= lo g_{10} (5 y)

lo g_{10} (x^{2} y^{5})

lo g_{3} (\frac{81}{y})

lo g_{10} (\frac{y ^{7}}{x z ^{3}})

2 + lo g_{2} (x) + 3 lo g_{2} (y)

lo g_{10} (3) + 2 lo g_{10} (5)

What is log_{10}(25x)-log_{10}(15x)+log_{10}(3y) ?
The solution to log_{10}(25x)-log_{10}(15x)+log_{10}(3y) is log_{10}(5y)