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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

0.52 \cdot ln (\frac{405.37}{451})

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

(ln (1) - ln (12)) + ln (M) + ln (L^{2})

- ln (2) + ln (7) - ln (6)

- \frac{1}{2} ln (\frac{y}{x}) - ln (x)

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