What is ln((x^6sqrt(x^2+2))/((x+2)^2)) ?

The solution to ln((x^6sqrt(x^2+2))/((x+2)^2)) is 6ln(x)+ln(sqrt(x^2+2))-2ln(x+2)

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simplify ln((x^6sqrt(x^2+2))/((x+2)^2))

simplify

ln (\frac{x ^{6} x ^{2} + 2}{( x + 2 ) ^{2}})

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

Solution steps

ln (\frac{x ^{6} x ^{2} + 2}{( x + 2 ) ^{2}})

Apply log rule:

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

ln (\frac{x ^{6} x ^{2} + 2}{( x + 2 ) ^{2}}) = ln (x^{6} x^{2} + 2) - ln ((x + 2)^{2})

= ln (x^{6} x^{2} + 2) - ln ((x + 2)^{2})

Apply log rule:

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

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

= ln (x^{6} x^{2} + 2) - 2 ln (x + 2)

Apply log rule:

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

ln (x^{6} x^{2} + 2) = ln (x^{6}) + ln (x^{2} + 2)

= ln (x^{6}) + ln (x^{2} + 2) - 2 ln (x + 2)

Apply log rule:

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

ln (x^{6}) = 6 ln (x)

= 6 ln (x) + ln (x^{2} + 2) - 2 ln (x + 2)

6 ln (x + 8) - 9 ln (x)

2 ln (x) + ln (y) - 0.5 ln (z)

ln (\frac{( x + 4 ) ^{7}}{x ^{7} x + 5})

30 lo g_{6} (3) + 30 lo g_{6} (2) - 6 lo g_{6} (11)

lo g_{b} (x yz) - 2 lo g_{b} (w)

What is ln((x^6sqrt(x^2+2))/((x+2)^2)) ?
The solution to ln((x^6sqrt(x^2+2))/((x+2)^2)) is 6ln(x)+ln(sqrt(x^2+2))-2ln(x+2)