What is ln((\sqrt[3]{x^2-1})/(yz^4)) ?

The solution to ln((\sqrt[3]{x^2-1})/(yz^4)) is ln(\sqrt[3]{x^2-1})-ln(y)-4ln(z)

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simplify ln((\sqrt[3]{x^2-1})/(yz^4))

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

ln (y z^{4}) = ln (y) + ln (z^{4})

Apply log rule:

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

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

- (ln (y) + 4 ln (z)) : - ln (y) - 4 ln (z)

lo g_{5} (\frac{5}{x})

lo g_{14} (14 x)

lo g_{4} (2 x)

lo g_{2} (\frac{x}{3})

2 lo g_{10} (x) + lo g_{10} (y) - lo g_{10} (z)

What is ln((\sqrt[3]{x^2-1})/(yz^4)) ?
The solution to ln((\sqrt[3]{x^2-1})/(yz^4)) is ln(\sqrt[3]{x^2-1})-ln(y)-4ln(z)