What is simplify-3log_{10}(z)+7log_{10}(x)-5log_{10}(y) ?

The solution to simplify-3log_{10}(z)+7log_{10}(x)-5log_{10}(y) is log_{10}((x^7)/(z^3y^5))

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simplify-3log_{10}(z)+7log_{10}(x)-5log_{10}(y)

simplify

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

lo g_{10} (\frac{x ^{7}}{z ^{3} y ^{5}})

Solution steps

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

- 3 lo g_{10} (z) = - lo g_{10} (z^{3})

7 lo g_{10} (x) = lo g_{10} (x^{7})

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

= - lo g_{10} (z^{3}) + lo g_{10} (x^{7}) - lo g_{10} (y^{5})

Apply log rule:

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

lo g_{10} (x^{7}) - lo g_{10} (z^{3}) = lo g_{10} (\frac{x ^{7}}{z ^{3}})

= lo g_{10} (\frac{x ^{7}}{z ^{3}}) - lo g_{10} (y^{5})

Apply log rule:

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

lo g_{10} (\frac{x ^{7}}{z ^{3}}) - lo g_{10} (y^{5}) = lo g_{10} (\frac{\frac{x ^{7}}{z ^{3}}}{y ^{5}})

= lo g_{10} (\frac{\frac{x ^{7}}{z ^{3}}}{y ^{5}})

Simplify

\frac{\frac{x ^{7}}{z ^{3}}}{y ^{5}} : \frac{x ^{7}}{z ^{3} y ^{5}}

= lo g_{10} (\frac{x ^{7}}{z ^{3} y ^{5}})

lo g_{6} (x z^{3})

4 lo g_{10} (a) + lo g_{10} (k)

lo g_{3} (\frac{x}{x + 2})

2 lo g_{x} (4) + lo g_{x} (3)

What is simplify-3log_{10}(z)+7log_{10}(x)-5log_{10}(y) ?
The solution to simplify-3log_{10}(z)+7log_{10}(x)-5log_{10}(y) is log_{10}((x^7)/(z^3y^5))