What is 3log_{6}(x)-7log_{6}(y) ?

The solution to 3log_{6}(x)-7log_{6}(y) is log_{6}((x^3)/(y^7))

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simplify 3log_{6}(x)-7log_{6}(y)

simplify

3 lo g_{6} (x) - 7 lo g_{6} (y)

lo g_{6} (\frac{x ^{3}}{y ^{7}})

Solution steps

3 lo g_{6} (x) - 7 lo g_{6} (y)

Apply log rule:

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

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

= lo g_{6} (x^{3}) - 7 lo g_{6} (y)

Apply log rule:

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

7 lo g_{6} (y) = lo g_{6} (y^{7})

= lo g_{6} (x^{3}) - lo g_{6} (y^{7})

Apply log rule:

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

lo g_{6} (x^{3}) - lo g_{6} (y^{7}) = lo g_{6} (\frac{x ^{3}}{y ^{7}})

= lo g_{6} (\frac{x ^{3}}{y ^{7}})

\frac{4}{5} ln (\frac{27027}{625})

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

\frac{ln ( 5 ) - ln ( 4 )}{ln ( 3 ) - ln ( 2 )}

lo g_{4} (\frac{1}{16} x)

ln (\frac{25}{7})

What is 3log_{6}(x)-7log_{6}(y) ?
The solution to 3log_{6}(x)-7log_{6}(y) is log_{6}((x^3)/(y^7))