What is expand ln(x^6(7-x)^{1/2}) ?

The solution to expand ln(x^6(7-x)^{1/2}) is 6ln(x)+1/2 ln(7-x)

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expand ln(x^6(7-x)^{1/2})

expand

ln (x^{6} (7 - x)^{\frac{1}{2}})

6 ln (x) + \frac{1}{2} ln (7 - x)

Solution steps

ln (x^{6} (7 - x)^{\frac{1}{2}})

Apply log rule:

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

ln (x^{6} (7 - x)^{\frac{1}{2}}) = ln (x^{6}) + ln ((7 - x)^{\frac{1}{2}})

= ln (x^{6}) + ln ((- x + 7)^{\frac{1}{2}})

Apply log rule:

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

ln (x^{6}) = 6 ln (x)

= 6 ln (x) + ln ((7 - x)^{\frac{1}{2}})

Apply log rule:

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

ln ((7 - x)^{\frac{1}{2}}) = \frac{1}{2} ln (7 - x)

= 6 ln (x) + \frac{1}{2} ln (7 - x)

4 lo g_{10} (g) - 2 lo g_{10} (h)

2 ln (x) - 2 - ln (y) 2

2 ln (5 x)

ln (\frac{16 e ^{- 4} 2}{( x + 1 ) ^{2}})

ln (\frac{x}{y ^{2} z ^{2}})

What is expand ln(x^6(7-x)^{1/2}) ?
The solution to expand ln(x^6(7-x)^{1/2}) is 6ln(x)+1/2 ln(7-x)