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

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

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simplify log_{10}((5x)/y)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

lo g_{10} (5 x) : lo g_{10} (5) + lo g_{10} (x)

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

ln (x) - 3 [ln (x - 7) + ln (x + 7)]

ln (\frac{e ^{5}}{9})

lo g_{b} (\frac{x ^{3} y}{z ^{5}})

lo g_{8} (a^{6} b^{5})

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