What is ln(x^{13}sqrt(7-x)) ?

The solution to ln(x^{13}sqrt(7-x)) is 13ln(x)+ln(sqrt(7-x))

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simplify ln(x^{13}sqrt(7-x))

simplify

ln (x^{13} 7 - x)

13 ln (x) + ln (7 - x)

Solution steps

ln (x^{13} 7 - x)

Apply log rule:

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

ln (x^{13} 7 - x) = ln (x^{13}) + ln (7 - x)

= ln (x^{13}) + ln (- x + 7)

Apply log rule:

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

ln (x^{13}) = 13 ln (x)

= 13 ln (x) + ln (7 - x)

ln (\frac{4 x 1 + 2 x}{( x - 4 ) ^{3}})

ln (\frac{x ^{9} x ^{2} + 7}{( x + 7 ) ^{7}})

ln ∣ 436700 ∣ - ln ∣ 105400 ∣

lo g_{3} (x^{2} - 16) - 2 lo g_{3} (x + 4)

lo g_{10} (\frac{1}{2 ^{n}})

What is ln(x^{13}sqrt(7-x)) ?
The solution to ln(x^{13}sqrt(7-x)) is 13ln(x)+ln(sqrt(7-x))