What is log_{e}(x^{10}sqrt(7-x)) ?

The solution to log_{e}(x^{10}sqrt(7-x)) is 10ln(x)+ln(sqrt(7-x))

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simplify log_{e}(x^{10}sqrt(7-x))

simplify

lo g_{e} (x^{10} 7 - x)

10 ln (x) + ln (7 - x)

Solution steps

lo g_{e} (x^{10} 7 - x)

Apply log rule:

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

lo g_{e} (x^{10} 7 - x) = lo g_{e} (x^{10}) + lo g_{e} (7 - x)

= lo g_{e} (x^{10}) + lo g_{e} (- x + 7)

Apply log rule:

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

lo g_{e} (x^{10}) = 10 lo g_{e} (x)

= 10 lo g_{e} (x) + lo g_{e} (7 - x)

Simplify

lo g_{e} (x) : ln (x)

= 10 ln (x) + lo g_{e} (- x + 7)

Apply log rule:

lo g_{e} (x) = ln (x)

= 10 ln (x) + ln (- x + 7)

ln (x + 3) + ln (1) - ln (2)

ln (\frac{1}{0.5}) - e^{- 0. 5^{3}}

lo g_{e} (\frac{x x + 1}{2 e ^{4}})

ln ((1 + 2 x) (1 + 3 x))

lo g_{10} (x) + 2 lo g_{10} (x + 1)

What is log_{e}(x^{10}sqrt(7-x)) ?
The solution to log_{e}(x^{10}sqrt(7-x)) is 10ln(x)+ln(sqrt(7-x))