What is log_{10}(x)+log_{10}(5)-log_{10}(y) ?

The solution to log_{10}(x)+log_{10}(5)-log_{10}(y) is log_{10}((5x)/y)

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simplify log_{10}(x)+log_{10}(5)-log_{10}(y)

simplify

lo g_{10} (x) + lo g_{10} (5) - lo g_{10} (y)

lo g_{10} (\frac{5 x}{y})

Solution steps

lo g_{10} (x) + lo g_{10} (5) - lo g_{10} (y)

Apply log rule:

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

lo g_{10} (x) + lo g_{10} (5) = lo g_{10} (x \cdot 5)

= lo g_{10} (x \cdot 5) - lo g_{10} (y)

Apply log rule:

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

lo g_{10} (x \cdot 5) - lo g_{10} (y) = lo g_{10} (\frac{x \cdot 5}{y})

= lo g_{10} (\frac{x \cdot 5}{y})

= lo g_{10} (\frac{5 x}{y})

3 ln (8) + 2 ln (x)

lo g_{3} (30 x (3 x + 4))

\frac{1}{2} (lo g_{10} (x) + lo g_{10} (y))

ln (y) + ln (x)

3 ln (x) - \frac{1}{9} ln (y)

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