What is ln(x^{14}sqrt(6-x)) ?

The solution to ln(x^{14}sqrt(6-x)) is 14ln(x)+ln(sqrt(6-x))

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simplify ln(x^{14}sqrt(6-x))

simplify

ln (x^{14} 6 - x)

14 ln (x) + ln (6 - x)

Solution steps

ln (x^{14} 6 - x)

Apply log rule:

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

ln (x^{14} 6 - x) = ln (x^{14}) + ln (6 - x)

= ln (x^{14}) + ln (- x + 6)

Apply log rule:

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

ln (x^{14}) = 14 ln (x)

= 14 ln (x) + ln (6 - x)

lo g_{10} (256 x^{8})

ln (x^{2} e^{- 2 x})

lo g_{10} (2) + lo g_{10} (5) - lo g_{10} (3)

lo g_{4} (3 x y)

2 lo g_{a} (7) + lo g_{a} (4) - lo g_{a} (10)

What is ln(x^{14}sqrt(6-x)) ?
The solution to ln(x^{14}sqrt(6-x)) is 14ln(x)+ln(sqrt(6-x))