What is expand ln((x^7sqrt(x^2+4))/((x+4)^6)) ?

The solution to expand ln((x^7sqrt(x^2+4))/((x+4)^6)) is 7ln(x)+ln(sqrt(x^2+4))-6ln(x+4)

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expand ln((x^7sqrt(x^2+4))/((x+4)^6))

expand

ln (\frac{x ^{7} x ^{2} + 4}{( x + 4 ) ^{6}})

7 ln (x) + ln (x^{2} + 4) - 6 ln (x + 4)

Solution steps

ln (\frac{x ^{7} x ^{2} + 4}{( x + 4 ) ^{6}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{x ^{7} x ^{2} + 4}{( x + 4 ) ^{6}}) = ln (x^{7} x^{2} + 4) - ln ((x + 4)^{6})

= ln (x^{7} x^{2} + 4) - ln ((x + 4)^{6})

Apply log rule:

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

ln ((x + 4)^{6}) = 6 ln (x + 4)

= ln (x^{7} x^{2} + 4) - 6 ln (x + 4)

Apply log rule:

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

ln (x^{7} x^{2} + 4) = ln (x^{7}) + ln (x^{2} + 4)

= ln (x^{7}) + ln (x^{2} + 4) - 6 ln (x + 4)

Apply log rule:

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

ln (x^{7}) = 7 ln (x)

= 7 ln (x) + ln (x^{2} + 4) - 6 ln (x + 4)

ln (\frac{1}{2} e^{x^{2}})

lo g_{10} (x) + 5 lo g_{10} (y)

5 ln (\frac{b}{24}) + 6 ln (\frac{b}{30}) + 9 ln (\frac{b}{40})

ln (\frac{3}{2.9})

ln (5 x sin (x))

What is expand ln((x^7sqrt(x^2+4))/((x+4)^6)) ?
The solution to expand ln((x^7sqrt(x^2+4))/((x+4)^6)) is 7ln(x)+ln(sqrt(x^2+4))-6ln(x+4)