What is log_{6}((x^4)/(y^7)) ?

The solution to log_{6}((x^4)/(y^7)) is 4log_{6}(x)-7log_{6}(y)

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simplify log_{6}((x^4)/(y^7))

simplify

lo g_{6} (\frac{x ^{4}}{y ^{7}})

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

Solution steps

lo g_{6} (\frac{x ^{4}}{y ^{7}})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{6} (\frac{x ^{4}}{y ^{7}}) = lo g_{6} (x^{4}) - lo g_{6} (y^{7})

= lo g_{6} (x^{4}) - lo g_{6} (y^{7})

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

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

= 4 lo g_{6} (x) - 7 lo g_{6} (y)

ln (\frac{1}{0.6})

1.526 - \frac{0.0592}{6} lo g_{10} (\frac{0.2 5 ^{2}}{2. 6 ^{3}})

ln (8) + 5 ln (x) + 3 ln (x^{2} + 9)

\frac{- 31 ln ( 3 ) - 14 ln ( 2 )}{2 ln ( 2 ) - ln ( 3 )}

ln (x - 2) - ln (x + 2)

What is log_{6}((x^4)/(y^7)) ?
The solution to log_{6}((x^4)/(y^7)) is 4log_{6}(x)-7log_{6}(y)