What is ln((t(t^2+1)^6)/(\sqrt[9]{2t-1)}) ?

The solution to ln((t(t^2+1)^6)/(\sqrt[9]{2t-1)}) is ln(t)+6ln(t^2+1)-ln(\sqrt[9]{2t-1})

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simplify ln((t(t^2+1)^6)/(\sqrt[9]{2t-1)})

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 (t (t^{2} + 1)^{6}) = ln (t) + ln ((t^{2} + 1)^{6})

Apply log rule:

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

ln ((t^{2} + 1)^{6}) = 6 ln (t^{2} + 1)

ln (x^{2}) + 2 ln (x)

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

lo g_{4} (5) + lo g_{4} (x) + lo g_{4} (y)

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

What is ln((t(t^2+1)^6)/(\sqrt[9]{2t-1)}) ?
The solution to ln((t(t^2+1)^6)/(\sqrt[9]{2t-1)}) is ln(t)+6ln(t^2+1)-ln(\sqrt[9]{2t-1})