What is ln(x^{10}sqrt(7-x)) ?

The solution to ln(x^{10}sqrt(7-x)) is 10ln(x)+ln(sqrt(7-x))

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simplify ln(x^{10}sqrt(7-x))

simplify

ln (x^{10} 7 - x)

10 ln (x) + ln (7 - x)

Solution steps

ln (x^{10} 7 - x)

Apply log rule:

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

ln (x^{10} 7 - x) = ln (x^{10}) + ln (7 - x)

= ln (x^{10}) + ln (- x + 7)

Apply log rule:

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

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

= 10 ln (x) + ln (7 - x)

ln (10) + 6 ln (x) + 3 ln (x^{2} + 2)

ln (\frac{( 0 - 1 )}{0.5})

ln (3) + ln (5)

lo g_{10} (z^{7} y)

lo g_{10} (z^{7} x)

What is ln(x^{10}sqrt(7-x)) ?
The solution to ln(x^{10}sqrt(7-x)) is 10ln(x)+ln(sqrt(7-x))