What is taylor ln(x)5 ?

The answer to taylor ln(x)5 is 5(x-1)-5/2 (x-1)^2+5/3 (x-1)^3-5/4 (x-1)^4+(x-1)^5+\ldots

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taylor ln(x)5

taylor

ln (x) 5

5 (x - 1) - \frac{5}{2} (x - 1)^{2} + \frac{5}{3} (x - 1)^{3} - \frac{5}{4} (x - 1)^{4} + (x - 1)^{5} + \dots

Solution steps

Apply the Taylor Formula

= 0 + \frac{\frac{d}{d x} ( ln ( x ) \cdot 5 ) ( 1 )}{1 !} (x - 1) + \frac{\frac{d ^{2}}{d x ^{2}} ( ln ( x ) \cdot 5 ) ( 1 )}{2 !} (x - 1)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ln ( x ) \cdot 5 ) ( 1 )}{3 !} (x - 1)^{3} + \dots

Evaluate Derivatives

= 0 + \frac{5}{1 !} (x - 1) + \frac{- 5}{2 !} (x - 1)^{2} + \frac{10}{3 !} (x - 1)^{3} + \frac{- 30}{4 !} (x - 1)^{4} + \frac{120}{5 !} (x - 1)^{5} + \dots

Refine

= 5 (x - 1) - \frac{5}{2} (x - 1)^{2} + \frac{5}{3} (x - 1)^{3} - \frac{5}{4} (x - 1)^{4} + (x - 1)^{5} + \dots

What is taylor ln(x)5 ?
The answer to taylor ln(x)5 is 5(x-1)-5/2 (x-1)^2+5/3 (x-1)^3-5/4 (x-1)^4+(x-1)^5+\ldots