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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

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

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

lo g_{10} (2 x y)

ln (x^{5}) - ln (x) + ln (\frac{1}{x})

lo g_{9} (x + 3) + lo g_{9} (x - 5)

lo g_{5} (5 x)

lo g_{10} (\frac{x}{100})

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