What is ln(x^{10}sqrt(6-x)) ?

The solution to ln(x^{10}sqrt(6-x)) is 10ln(x)+ln(sqrt(6-x))

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simplify ln(x^{10}sqrt(6-x))

simplify

ln (x^{10} 6 - x)

10 ln (x) + ln (6 - x)

Solution steps

ln (x^{10} 6 - x)

Apply log rule:

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

ln (x^{10} 6 - x) = ln (x^{10}) + ln (6 - x)

= ln (x^{10}) + ln (- x + 6)

Apply log rule:

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

ln (x^{10}) = 10 ln (x)

= 10 ln (x) + ln (6 - x)

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

ln ((sin (2 x))^{2})

lo g_{10} (\frac{y ^{3}}{x})

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

What is ln(x^{10}sqrt(6-x)) ?
The solution to ln(x^{10}sqrt(6-x)) is 10ln(x)+ln(sqrt(6-x))