What is 2(log_{6}(x)+3log_{6}(y)-4log_{6}(z)) ?

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

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simplify 2(log_{6}(x)+3log_{6}(y)-4log_{6}(z))

simplify

2 (lo g_{6} (x) + 3 lo g_{6} (y) - 4 lo g_{6} (z))

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

Solution steps

2 (lo g_{6} (x) + 3 lo g_{6} (y) - 4 lo g_{6} (z))

Apply log rule:

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

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

= 2 (lo g_{6} (x) + lo g_{6} (y^{3}) - 4 lo g_{6} (z))

Apply log rule:

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

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

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

Apply log rule:

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

4 lo g_{6} (z) = lo g_{6} (z^{4})

= 2 (- lo g_{6} (z^{4}) + lo g_{6} (x y^{3}))

Apply log rule:

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

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

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

ln (\frac{x}{x - 2})

ln (t - 1) - ln (t + 3)

6.1 + lo g_{10} (\frac{31}{0.03 \cdot 71})

\frac{9}{10} ln (30) - \frac{12}{5} ln (40)

0.14 - \frac{0.0591}{2} \cdot lo g_{10} (\frac{1}{3})

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