What is 5ln(x)+ln(sqrt(x^2+7))-9ln(x+7) ?

The solution to 5ln(x)+ln(sqrt(x^2+7))-9ln(x+7) is ln((x^5sqrt(x^2+7))/((x+7)^9))

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simplify 5ln(x)+ln(sqrt(x^2+7))-9ln(x+7)

simplify

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

ln (\frac{x ^{5} x ^{2} + 7}{( x + 7 ) ^{9}})

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

5 ln (x) = ln (x^{5})

= ln (x^{5}) + ln (x^{2} + 7) - 9 ln (x + 7)

Apply log rule:

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

ln (x^{5}) + ln (x^{2} + 7) = ln (x^{5} x^{2} + 7)

= ln (x^{5} x^{2} + 7) - 9 ln (x + 7)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= ln (x^{5} x^{2} + 7) - ln ((x + 7)^{9})

Apply log rule:

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

ln (x^{5} x^{2} + 7) - ln ((x + 7)^{9}) = ln (\frac{x ^{5} x ^{2} + 7}{( x + 7 ) ^{9}})

= ln (\frac{x ^{5} x ^{2} + 7}{( x + 7 ) ^{9}})

lo g_{10} (3.436 + 1) - lo g_{10} (1.718)

(0.717) ln (\frac{252}{17})

ln (\frac{2 x}{3}) + \frac{1}{8} ln (\frac{x}{4}) + \frac{3}{8} ln (\frac{3 x}{4})

ln (a e^{- b x})

- 3 ln (x^{2} + 1) - ln (sin (x))

What is 5ln(x)+ln(sqrt(x^2+7))-9ln(x+7) ?
The solution to 5ln(x)+ln(sqrt(x^2+7))-9ln(x+7) is ln((x^5sqrt(x^2+7))/((x+7)^9))