What is expand log_{6}((5x)/(y^4)) ?

The solution to expand log_{6}((5x)/(y^4)) is log_{6}(5)+log_{6}(x)-4log_{6}(y)

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expand log_{6}((5x)/(y^4))

expand

lo g_{6} (\frac{5 x}{y ^{4}})

lo g_{6} (5) + lo g_{6} (x) - 4 lo g_{6} (y)

Solution steps

lo g_{6} (\frac{5 x}{y ^{4}})

Apply log rule:

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

lo g_{6} (\frac{5 x}{y ^{4}}) = lo g_{6} (5 x) - lo g_{6} (y^{4})

= lo g_{6} (5 x) - lo g_{6} (y^{4})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= lo g_{6} (5 x) - 4 lo g_{6} (y)

Apply log rule:

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

lo g_{6} (5 x) = lo g_{6} (5) + lo g_{6} (x)

= lo g_{6} (5) + lo g_{6} (x) - 4 lo g_{6} (y)

\frac{7}{12} lo g_{2} (\frac{12}{7}) + \frac{5}{12} lo g_{2} (\frac{12}{5})

ln (5) + \frac{1}{5} ln (4 - x^{2}) - ln (x)

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

ln (A e^{(- \frac{e}{RT})})

\frac{5 ln ( 2 )}{ln ( \frac{533}{500} )}

What is expand log_{6}((5x)/(y^4)) ?
The solution to expand log_{6}((5x)/(y^4)) is log_{6}(5)+log_{6}(x)-4log_{6}(y)