What is ln((x^5sqrt(x+2))/(x+8)) ?

The solution to ln((x^5sqrt(x+2))/(x+8)) is 5ln(x)+ln(sqrt(x+2))-ln(x+8)

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simplify ln((x^5sqrt(x+2))/(x+8))

simplify

ln (\frac{x ^{5} x + 2}{x + 8})

5 ln (x) + ln (x + 2) - ln (x + 8)

Solution steps

ln (\frac{x ^{5} x + 2}{x + 8})

Apply log rule:

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

ln (\frac{x ^{5} x + 2}{x + 8}) = ln (x^{5} x + 2) - ln (x + 8)

= ln (x^{5} x + 2) - ln (x + 8)

Apply log rule:

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

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

= ln (x^{5}) + ln (x + 2) - ln (x + 8)

Apply log rule:

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

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

= 5 ln (x) + ln (x + 2) - ln (x + 8)

\frac{1}{5} ln (\frac{x - 1}{x ^{2} - x + 1})

lo g_{10} (\frac{2 x ( 1 - 5 x ) ^{\frac{3}{2}}}{( x + 4 ) ^{3}})

ln (\frac{0.075}{0.06})

ln (\frac{2}{e ^{(- 1)} - e})

19 x + ln (19) + ln (x)

What is ln((x^5sqrt(x+2))/(x+8)) ?
The solution to ln((x^5sqrt(x+2))/(x+8)) is 5ln(x)+ln(sqrt(x+2))-ln(x+8)