What is log_{6}(x)-2log_{6}(y)+log_{6}(z) ?

The solution to log_{6}(x)-2log_{6}(y)+log_{6}(z) is log_{6}((xz)/(y^2))

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simplify log_{6}(x)-2log_{6}(y)+log_{6}(z)

simplify

lo g_{6} (x) - 2 lo g_{6} (y) + lo g_{6} (z)

lo g_{6} (\frac{x z}{y ^{2}})

Solution steps

lo g_{6} (x) - 2 lo g_{6} (y) + lo g_{6} (z)

Apply log rule:

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

2 lo g_{6} (y) = lo g_{6} (y^{2})

= lo g_{6} (x) - lo g_{6} (y^{2}) + lo g_{6} (z)

Apply log rule:

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

lo g_{6} (x) - lo g_{6} (y^{2}) = lo g_{6} (\frac{x}{y ^{2}})

= lo g_{6} (\frac{x}{y ^{2}}) + lo g_{6} (z)

Apply log rule:

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

lo g_{6} (\frac{x}{y ^{2}}) + lo g_{6} (z) = lo g_{6} (\frac{x}{y ^{2}} z)

= lo g_{6} (\frac{x}{y ^{2}} z)

Multiply fractions:

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

= lo g_{6} (\frac{x z}{y ^{2}})

- lo g_{10} (5 \cdot 1 0^{- 3})

2 ln (x) + 3 ln (y) - 5 ln (z)

ln (x^{9}) - \frac{1}{4} ln (x^{- 7})

6 ln (x) + 4 ln (y) - 2 ln (z)

What is log_{6}(x)-2log_{6}(y)+log_{6}(z) ?
The solution to log_{6}(x)-2log_{6}(y)+log_{6}(z) is log_{6}((xz)/(y^2))