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

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

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

simplify

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

lo g_{10} (y)

Solution steps

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

Apply log rule:

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

lo g_{10} (\frac{x}{y}) + lo g_{10} (\frac{y ^{2}}{x}) = lo g_{10} (\frac{x}{y} \cdot \frac{y ^{2}}{x})

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

Simplify

\frac{x}{y} \cdot \frac{y ^{2}}{x} : y

= lo g_{10} (y)

ln (4) + ln (8) - ln (16)

4 lo g_{4} (8) - lo g_{4} (3)

3 ln (x - 1) + 4 ln (x - 6) - \frac{1}{3} ln (2 x - 1)

\frac{6}{lo g _{10} ( 0.593 ) - lo g _{10} ( 0.451 )}

7 lo g_{5} (x) + 3 lo g_{5} (y^{4})

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