What is ln(x^{10}sqrt(2-x)) ?

The solution to ln(x^{10}sqrt(2-x)) is 10ln(x)+ln(sqrt(2-x))

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simplify ln(x^{10}sqrt(2-x))

simplify

ln (x^{10} 2 - x)

10 ln (x) + ln (2 - x)

Solution steps

ln (x^{10} 2 - x)

Apply log rule:

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

ln (x^{10} 2 - x) = ln (x^{10}) + ln (2 - x)

= ln (x^{10}) + ln (- x + 2)

Apply log rule:

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

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

= 10 ln (x) + ln (2 - x)

lo g_{5} (x) - 8 lo g_{5} (y) - 9 lo g_{5} (z)

lo g_{10} (x^{3} y^{6})

lo g_{10} (30) + lo g_{10} (5)

lo g_{x} (\frac{a + 2}{a + 3})

lo g_{10} (2) + lo g_{10} (\frac{3}{2})

What is ln(x^{10}sqrt(2-x)) ?
The solution to ln(x^{10}sqrt(2-x)) is 10ln(x)+ln(sqrt(2-x))