What is ln(x^{12}sqrt(4-x)) ?

The solution to ln(x^{12}sqrt(4-x)) is 12ln(x)+ln(sqrt(4-x))

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simplify ln(x^{12}sqrt(4-x))

simplify

ln (x^{12} 4 - x)

12 ln (x) + ln (4 - x)

Solution steps

ln (x^{12} 4 - x)

Apply log rule:

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

ln (x^{12} 4 - x) = ln (x^{12}) + ln (4 - x)

= ln (x^{12}) + ln (- x + 4)

Apply log rule:

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

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

= 12 ln (x) + ln (4 - x)

50 \cdot ln (\frac{54.8}{72})

- lo g_{10} (3.89 \cdot 1 0^{- 4})

ln (x + 1) + ln (x - 1)

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

3 lo g_{10} (m) + 2 lo g_{10} (n)

What is ln(x^{12}sqrt(4-x)) ?
The solution to ln(x^{12}sqrt(4-x)) is 12ln(x)+ln(sqrt(4-x))