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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

ln ((x + 7)^{9}) = 9 ln (x + 7)

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (x^{2}) = 2 ln (x)

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

lo g_{10} (\frac{x ^{4} y}{z})

lo g_{7} (4 yz)

lo g_{b} (5 x \cdot 2 y)

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