What is log_{10}(x)-3log_{10}(y)-2log_{10}(z) ?

The solution to log_{10}(x)-3log_{10}(y)-2log_{10}(z) is log_{10}(x/(y^3z^2))

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simplify log_{10}(x)-3log_{10}(y)-2log_{10}(z)

simplify

lo g_{10} (x) - 3 lo g_{10} (y) - 2 lo g_{10} (z)

lo g_{10} (\frac{x}{y ^{3} z ^{2}})

Solution steps

lo g_{10} (x) - 3 lo g_{10} (y) - 2 lo g_{10} (z)

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

- 2 lo g_{10} (z) = - lo g_{10} (z^{2})

= lo g_{10} (x) - lo g_{10} (y^{3}) - lo g_{10} (z^{2})

Apply log rule:

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

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

= lo g_{10} (\frac{x}{y ^{3}}) - lo g_{10} (z^{2})

Apply log rule:

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

lo g_{10} (\frac{x}{y ^{3}}) - lo g_{10} (z^{2}) = lo g_{10} (\frac{\frac{x}{y ^{3}}}{z ^{2}})

= lo g_{10} (\frac{\frac{x}{y ^{3}}}{z ^{2}})

Simplify

\frac{\frac{x}{y ^{3}}}{z ^{2}} : \frac{x}{y ^{3} z ^{2}}

= lo g_{10} (\frac{x}{y ^{3} z ^{2}})

\frac{1}{3} lo g_{10} (x) + 2 lo g_{10} (y)

lo g_{6} (5 z)

lo g_{6} (5 x)

lo g_{8} (\frac{w ^{4} x ^{2}}{yz})

lo g_{10} (512) - lo g_{10} (366)

What is log_{10}(x)-3log_{10}(y)-2log_{10}(z) ?
The solution to log_{10}(x)-3log_{10}(y)-2log_{10}(z) is log_{10}(x/(y^3z^2))