What is ln((x^7sqrt(x^2+4))/((x+4)^9)) ?

The solution to ln((x^7sqrt(x^2+4))/((x+4)^9)) is 7ln(x)+ln(sqrt(x^2+4))-9ln(x+4)

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simplify ln((x^7sqrt(x^2+4))/((x+4)^9))

simplify

ln (\frac{x ^{7} x ^{2} + 4}{( x + 4 ) ^{9}})

7 ln (x) + ln (x^{2} + 4) - 9 ln (x + 4)

Solution steps

ln (\frac{x ^{7} x ^{2} + 4}{( x + 4 ) ^{9}})

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 ) ^{9}}) = ln (x^{7} x^{2} + 4) - ln ((x + 4)^{9})

= ln (x^{7} x^{2} + 4) - ln ((x + 4)^{9})

Apply log rule:

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

ln ((x + 4)^{9}) = 9 ln (x + 4)

= ln (x^{7} x^{2} + 4) - 9 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) - 9 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) - 9 ln (x + 4)

3 lo g_{2} (a) + 2 lo g_{2} (b)

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10 lo g_{10} (\frac{i}{1 0 ^{12} i _{0}})

ln (\frac{2}{80})

600 ln (600) + 400 ln (400)

What is ln((x^7sqrt(x^2+4))/((x+4)^9)) ?
The solution to ln((x^7sqrt(x^2+4))/((x+4)^9)) is 7ln(x)+ln(sqrt(x^2+4))-9ln(x+4)