What is log_{10}((5x)/(7-x)) ?

The solution to log_{10}((5x)/(7-x)) is log_{10}(5)+log_{10}(x)-log_{10}(7-x)

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simplify log_{10}((5x)/(7-x))

simplify

lo g_{10} (\frac{5 x}{7 - x})

lo g_{10} (5) + lo g_{10} (x) - lo g_{10} (7 - x)

Solution steps

lo g_{10} (\frac{5 x}{7 - x})

Apply log rule:

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

lo g_{10} (\frac{5 x}{7 - x}) = lo g_{10} (5 x) - lo g_{10} (7 - x)

= lo g_{10} (5 x) - lo g_{10} (7 - x)

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} (7 - x)

lo g_{4} (16 a)

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

lo g_{10} (y) + 12 lo g_{10} (z)

lo g_{2} (\frac{x}{8})

lo g_{2} (2 x)

What is log_{10}((5x)/(7-x)) ?
The solution to log_{10}((5x)/(7-x)) is log_{10}(5)+log_{10}(x)-log_{10}(7-x)