What is ln((((x-4)^2)/(x^2-1))^{2/3}) ?

The solution to ln((((x-4)^2)/(x^2-1))^{2/3}) is 2/3 (2ln(x-4)-ln(x^2-1))

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simplify ln((((x-4)^2)/(x^2-1))^{2/3})

simplify

ln (\frac{( x - 4 ) ^{2}}{x ^{2} - 1})^{\frac{2}{3}}

\frac{2}{3} (2 ln (x - 4) - ln (x^{2} - 1))

Solution steps

ln (\frac{( x - 4 ) ^{2}}{x ^{2} - 1})^{\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{( x - 4 ) ^{2}}{x ^{2} - 1})

Simplify

ln (\frac{( x - 4 ) ^{2}}{x ^{2} - 1}) : 2 ln (x - 4) - ln (x^{2} - 1)

= \frac{2}{3} (2 ln (x - 4) - ln (x^{2} - 1))

9 (3 - 4)^{2} + (\frac{1 - 1}{2})^{2}

(- 5) (- 4)

\frac{( x ^{2} - 5 x y - 14 y ^{2} )}{( x - 7 y )}

[\frac{b ^{8} \cdot ( a ^{3} ) ^{4}}{2 \cdot b ^{4} \cdot a ^{6}}]^{3}

5 + 75

What is ln((((x-4)^2)/(x^2-1))^{2/3}) ?
The solution to ln((((x-4)^2)/(x^2-1))^{2/3}) is 2/3 (2ln(x-4)-ln(x^2-1))