What is ln((x^6sqrt(x^2+3))/((x+3)^4)) ?

The solution to ln((x^6sqrt(x^2+3))/((x+3)^4)) is 6ln(x)+ln(sqrt(x^2+3))-4ln(x+3)

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simplify ln((x^6sqrt(x^2+3))/((x+3)^4))

simplify

ln (\frac{x ^{6} x ^{2} + 3}{( x + 3 ) ^{4}})

6 ln (x) + ln (x^{2} + 3) - 4 ln (x + 3)

Solution steps

ln (\frac{x ^{6} x ^{2} + 3}{( x + 3 ) ^{4}})

Apply log rule:

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

ln (\frac{x ^{6} x ^{2} + 3}{( x + 3 ) ^{4}}) = ln (x^{6} x^{2} + 3) - ln ((x + 3)^{4})

= ln (x^{6} x^{2} + 3) - ln ((x + 3)^{4})

Apply log rule:

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

ln ((x + 3)^{4}) = 4 ln (x + 3)

= ln (x^{6} x^{2} + 3) - 4 ln (x + 3)

Apply log rule:

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

ln (x^{6} x^{2} + 3) = ln (x^{6}) + ln (x^{2} + 3)

= ln (x^{6}) + ln (x^{2} + 3) - 4 ln (x + 3)

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} + 3) - 4 ln (x + 3)

lo g_{12} (A) - lo g_{12} (C)

2 (ln (ln (\frac{3}{2})) + ln (ln (\frac{5}{2})))

lo g_{3} (27 x^{2})

6 lo g_{5} (u) + 9 lo g_{5} (v)

lo g_{10} (\frac{x + 2}{x - 1})

What is ln((x^6sqrt(x^2+3))/((x+3)^4)) ?
The solution to ln((x^6sqrt(x^2+3))/((x+3)^4)) is 6ln(x)+ln(sqrt(x^2+3))-4ln(x+3)