What is ln(((x-2)^2)/(\sqrt[5]{x^2+1)(x+5)^5}) ?

The solution to ln(((x-2)^2)/(\sqrt[5]{x^2+1)(x+5)^5}) is 2ln(x-2)-ln(\sqrt[5]{x^2+1})-5ln(x+5)

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simplify ln(((x-2)^2)/(\sqrt[5]{x^2+1)(x+5)^5})

simplify

Solution steps

Apply log rule:

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

Apply log rule:

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

ln ((x - 2)^{2}) = 2 ln (x - 2)

Apply log rule:

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

Apply log rule:

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

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

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

lo g_{5} ((\frac{x}{2 y})^{8})

\frac{( ln ( 0.25 ) + ln ( 0.5 ) + ln ( 0.75 ) ) \cdot 2 \cdot 0.25}{2}

\frac{ln ( 5.999 ) - ln ( 6 )}{5.999 - 6}

ln (3.5 \cdot 1 0^{- 14})

What is ln(((x-2)^2)/(\sqrt[5]{x^2+1)(x+5)^5}) ?
The solution to ln(((x-2)^2)/(\sqrt[5]{x^2+1)(x+5)^5}) is 2ln(x-2)-ln(\sqrt[5]{x^2+1})-5ln(x+5)