What is log_{10}(x^2)-log_{10}(x)y+4log_{10}(y) ?

The solution to log_{10}(x^2)-log_{10}(x)y+4log_{10}(y) is log_{10}(x^{2-y}y^4)

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simplify log_{10}(x^2)-log_{10}(x)y+4log_{10}(y)

simplify

lo g_{10} (x^{2}) - lo g_{10} (x) y + 4 lo g_{10} (y)

lo g_{10} (x^{2 - y} y^{4})

Solution steps

lo g_{10} (x^{2}) - lo g_{10} (x) y + 4 lo g_{10} (y)

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

4 lo g_{10} (y) = lo g_{10} (y^{4})

= lo g_{10} (x^{2}) - lo g_{10} (x^{y}) + lo g_{10} (y^{4})

Apply log rule:

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

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

= lo g_{10} (\frac{x ^{2}}{x ^{y}}) + lo g_{10} (y^{4})

Apply log rule:

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

lo g_{10} (\frac{x ^{2}}{x ^{y}}) + lo g_{10} (y^{4}) = lo g_{10} (\frac{x ^{2}}{x ^{y}} y^{4})

= lo g_{10} (\frac{x ^{2}}{x ^{y}} y^{4})

Simplify

\frac{x ^{2}}{x ^{y}} y^{4} : x^{2 - y} y^{4}

= lo g_{10} (x^{2 - y} y^{4})

lo g_{5} (x \cdot y \cdot z^{4})

lo g_{5} (x^{2} - 1) - lo g_{5} (x - 1)

lo g_{10} (\frac{z ^{2}}{x y ^{4}})

lo g_{10} (0.24 x 1 0^{6})

lo g_{2} (\frac{a ^{2} - 4}{9})

What is log_{10}(x^2)-log_{10}(x)y+4log_{10}(y) ?
The solution to log_{10}(x^2)-log_{10}(x)y+4log_{10}(y) is log_{10}(x^{2-y}y^4)