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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

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ln (10) - ln (20)

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

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