What is ln((x^4sqrt(x^2+3))/((x+3)^5)) ?

The solution to ln((x^4sqrt(x^2+3))/((x+3)^5)) is 4ln(x)+ln(sqrt(x^2+3))-5ln(x+3)

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simplify ln((x^4sqrt(x^2+3))/((x+3)^5))

simplify

ln (\frac{x ^{4} x ^{2} + 3}{( x + 3 ) ^{5}})

4 ln (x) + ln (x^{2} + 3) - 5 ln (x + 3)

Solution steps

ln (\frac{x ^{4} x ^{2} + 3}{( x + 3 ) ^{5}})

Apply log rule:

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

ln (\frac{x ^{4} x ^{2} + 3}{( x + 3 ) ^{5}}) = ln (x^{4} x^{2} + 3) - ln ((x + 3)^{5})

= ln (x^{4} x^{2} + 3) - ln ((x + 3)^{5})

Apply log rule:

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

ln ((x + 3)^{5}) = 5 ln (x + 3)

= ln (x^{4} x^{2} + 3) - 5 ln (x + 3)

Apply log rule:

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

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

= ln (x^{4}) + ln (x^{2} + 3) - 5 ln (x + 3)

Apply log rule:

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

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

= 4 ln (x) + ln (x^{2} + 3) - 5 ln (x + 3)

lo g_{2} (\frac{8}{x})

ln (\frac{x ^{2}}{y})

lo g_{10} (x - 3) + lo g_{10} (x + 3)

lo g_{10} (\frac{x ^{4}}{y ^{2}})

7 lo g_{b} (x) + 6 lo g_{b} (z)

What is ln((x^4sqrt(x^2+3))/((x+3)^5)) ?
The solution to ln((x^4sqrt(x^2+3))/((x+3)^5)) is 4ln(x)+ln(sqrt(x^2+3))-5ln(x+3)