What is ln(((3x(2x-1)^{1/3})/((5-x)^2))^{2/3}) ?

The solution to ln(((3x(2x-1)^{1/3})/((5-x)^2))^{2/3}) is 2/3 (ln(3x)+1/3 ln(2x-1)-2ln(-x+5))

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simplify ln(((3x(2x-1)^{1/3})/((5-x)^2))^{2/3})

simplify

ln (\frac{3 x ( 2 x - 1 ) ^{\frac{1}{3}}}{( 5 - x ) ^{2}})^{\frac{2}{3}}

\frac{2}{3} (ln (3 x) + \frac{1}{3} ln (2 x - 1) - 2 ln (- x + 5))

Solution steps

ln (\frac{3 x ( 2 x - 1 ) ^{\frac{1}{3}}}{( 5 - x ) ^{2}})^{\frac{2}{3}}

Apply log rule

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

assuming

x \geq 0

= \frac{2}{3} ln (\frac{3 x ( 2 x - 1 ) ^{\frac{1}{3}}}{( - x + 5 ) ^{2}})

Simplify

ln (\frac{3 x ( 2 x - 1 ) ^{\frac{1}{3}}}{( 5 - x ) ^{2}}) : ln (3 x (2 x - 1)^{\frac{1}{3}}) - 2 ln (- x + 5)

= \frac{2}{3} (ln (3 x (2 x - 1)^{\frac{1}{3}}) - 2 ln (- x + 5))

ln (3 x (2 x - 1)^{\frac{1}{3}}) = ln (3 x) + \frac{1}{3} ln (2 x - 1)

= \frac{2}{3} (ln (3 x) + \frac{1}{3} ln (2 x - 1) - 2 ln (- x + 5))

(8 - 6 i) (- 4 + 2 i)

\frac{120}{60}

24 x

250 h^{3}

\frac{2}{3} \cdot 60

What is ln(((3x(2x-1)^{1/3})/((5-x)^2))^{2/3}) ?
The solution to ln(((3x(2x-1)^{1/3})/((5-x)^2))^{2/3}) is 2/3 (ln(3x)+1/3 ln(2x-1)-2ln(-x+5))