What is ln(x^{12}sqrt(6-x)) ?

The solution to ln(x^{12}sqrt(6-x)) is 12ln(x)+ln(sqrt(6-x))

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simplify ln(x^{12}sqrt(6-x))

simplify

ln (x^{12} 6 - x)

12 ln (x) + ln (6 - x)

Solution steps

ln (x^{12} 6 - x)

Apply log rule:

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

ln (x^{12} 6 - x) = ln (x^{12}) + ln (6 - x)

= ln (x^{12}) + ln (- x + 6)

Apply log rule:

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

ln (x^{12}) = 12 ln (x)

= 12 ln (x) + ln (6 - x)

lo g_{10} (7) + lo g_{10} (4)

lo g_{a} (\frac{x y}{z ^{2}})

ln (x e^{5 x})

lo g_{3} (\frac{a}{b})

lo g_{2} (15) + 6 lo g_{2} (x) - \frac{4}{3} lo g_{2} (x) - \frac{1}{3} lo g_{2} (x + 3)

What is ln(x^{12}sqrt(6-x)) ?
The solution to ln(x^{12}sqrt(6-x)) is 12ln(x)+ln(sqrt(6-x))