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

The solution to ln(((x^2+6)/(x^3+4))^{3/2}) is 3/2 ln((x^2+6)/(x^3+4))

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

simplify

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

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

Solution steps

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

Apply log rule

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

assuming

x \geq 0

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

x^{- 3} \cdot (5 + 3 x)

∣ - 6 x + 4 y ∣

\frac{lo g _{10} ( 1 )}{x}

5.5352 E 17 - 1 x^{1}

16 (3 x^{2} + 5 x - 9) (3 x - 5)

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