What is log_{6}((x^4e^2)/(sqrt(6x+6))) ?

The solution to log_{6}((x^4e^2)/(sqrt(6x+6))) is 4log_{6}(x)+2log_{6}(e)-log_{6}(sqrt(6x+6))

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simplify log_{6}((x^4e^2)/(sqrt(6x+6)))

simplify

lo g_{6} (\frac{x ^{4} e ^{2}}{6 x + 6})

4 lo g_{6} (x) + 2 lo g_{6} (e) - lo g_{6} (6 x + 6)

Solution steps

lo g_{6} (\frac{x ^{4} e ^{2}}{6 x + 6})

Apply log rule:

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

lo g_{6} (\frac{x ^{4} e ^{2}}{6 x + 6}) = lo g_{6} (x^{4} e^{2}) - lo g_{6} (6 x + 6)

= lo g_{6} (e^{2} x^{4}) - lo g_{6} (6 x + 6)

Apply log rule:

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

lo g_{6} (x^{4} e^{2}) = lo g_{6} (x^{4}) + lo g_{6} (e^{2})

= lo g_{6} (x^{4}) + lo g_{6} (e^{2}) - lo g_{6} (6 x + 6)

Apply log rule:

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

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

= 4 lo g_{6} (x) + lo g_{6} (e^{2}) - lo g_{6} (6 x + 6)

Apply log rule:

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

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

= 4 lo g_{6} (x) + 2 lo g_{6} (e) - lo g_{6} (6 x + 6)

ln (\frac{( a ^{2} + h ^{2} )}{2 h})

- lo g_{10} (\frac{1 0 ^{- 14}}{4.54 \cdot 1 0 ^{- 3}})

ln (\frac{104}{114})

lo g_{10} (\frac{( y ^{5} )}{z ^{2} x ^{3}})

lo g_{a} (\frac{( a ^{4} ) b}{c ^{3}})

What is log_{6}((x^4e^2)/(sqrt(6x+6))) ?
The solution to log_{6}((x^4e^2)/(sqrt(6x+6))) is 4log_{6}(x)+2log_{6}(e)-log_{6}(sqrt(6x+6))