What is 3log_{6}(z)+2(log_{6}(x)-2log_{6}(y)) ?

The solution to 3log_{6}(z)+2(log_{6}(x)-2log_{6}(y)) is log_{6}((z^3x^2)/(y^4))

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simplify 3log_{6}(z)+2(log_{6}(x)-2log_{6}(y))

simplify

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

lo g_{6} (\frac{z ^{3} x ^{2}}{y ^{4}})

Solution steps

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

Apply log rule:

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

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

= 3 lo g_{6} (z) + 2 (lo g_{6} (x) - lo g_{6} (y^{2}))

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}})

= 3 lo g_{6} (z) + 2 lo g_{6} (\frac{x}{y ^{2}})

Apply log rule:

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

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

= lo g_{6} (z^{3}) + 2 lo g_{6} (\frac{x}{y ^{2}})

Apply log rule:

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

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

= lo g_{6} (z^{3}) + lo g_{6} ((\frac{x}{y ^{2}})^{2})

Apply log rule:

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

lo g_{6} (z^{3}) + lo g_{6} ((\frac{x}{y ^{2}})^{2}) = lo g_{6} ((\frac{x}{y ^{2}})^{2} z^{3})

= lo g_{6} ((\frac{x}{y ^{2}})^{2} z^{3})

Simplify

z^{3} (\frac{x}{y ^{2}})^{2} : \frac{z ^{3} x ^{2}}{y ^{4}}

= lo g_{6} (\frac{z ^{3} x ^{2}}{y ^{4}})

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

\frac{1}{2} ln (3 c) + \frac{1}{2} ln (4) d - 2 ln (5 e)

- 5137.521 + 1239.973 ln (\frac{2018}{30})

ln (0.6889 \cdot π)

lo g_{16} (\frac{1}{18})

What is 3log_{6}(z)+2(log_{6}(x)-2log_{6}(y)) ?
The solution to 3log_{6}(z)+2(log_{6}(x)-2log_{6}(y)) is log_{6}((z^3x^2)/(y^4))