What is ln(x^{12}sqrt(5-x)) ?

The solution to ln(x^{12}sqrt(5-x)) is 12ln(x)+ln(sqrt(5-x))

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simplify ln(x^{12}sqrt(5-x))

simplify

ln (x^{12} 5 - x)

12 ln (x) + ln (5 - x)

Solution steps

ln (x^{12} 5 - x)

Apply log rule:

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

ln (x^{12} 5 - x) = ln (x^{12}) + ln (5 - x)

= ln (x^{12}) + ln (- x + 5)

Apply log rule:

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

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

= 12 ln (x) + ln (5 - x)

lo g_{8} (64 x^{3})

- lo g_{10} (5.6 \cdot 1 0^{- 5})

lo g_{b} (x) + lo g_{b} (y)

lo g_{2} (\frac{5 y}{z})

- (\frac{2}{3} lo g_{2} (\frac{2}{3}) + \frac{1}{3} lo g_{2} (\frac{1}{3}))

What is ln(x^{12}sqrt(5-x)) ?
The solution to ln(x^{12}sqrt(5-x)) is 12ln(x)+ln(sqrt(5-x))