What is log_{10}((5x)/(y^2)) ?

The solution to log_{10}((5x)/(y^2)) is log_{10}(5)+log_{10}(x)-2log_{10}(y)

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simplify log_{10}((5x)/(y^2))

simplify

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

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

Solution steps

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

Apply log rule:

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

lo g_{10} (\frac{5 x}{y ^{2}}) = lo g_{10} (5 x) - lo g_{10} (y^{2})

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

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

lo g_{10} (y^{2}) = 2 lo g_{10} (y)

= lo g_{10} (5) + lo g_{10} (x) - 2 lo g_{10} (y)

lo g_{10} (\frac{z ^{3}}{x ^{5} y})

ln (\frac{6}{7})

lo g_{10} (5) - lo g_{10} (20)

2 \cdot lo g_{10} (x - 4) + lo g_{10} (3 x)

3 lo g_{10} (x) + 4 lo g_{10} (y)

What is log_{10}((5x)/(y^2)) ?
The solution to log_{10}((5x)/(y^2)) is log_{10}(5)+log_{10}(x)-2log_{10}(y)