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

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

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

simplify

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

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

Solution steps

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

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

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

Apply log rule:

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

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

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

ln ∣ 436700 ∣ - ln ∣ 105400 ∣

lo g_{3} (x^{2} - 16) - 2 lo g_{3} (x + 4)

lo g_{10} (\frac{1}{2 ^{n}})

- lo g_{10} (8.3 \cdot 1 0^{- 5})

lo g_{10} (14) - lo g_{10} (7)

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