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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (7) - 3 ln (x)

ln (2.01 \cdot 1 0^{- 2})

\frac{1}{2} lo g_{7} (x) + \frac{1}{2} lo g_{7} (y)

ln (\frac{h}{a})

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

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