What is taylor ln(3x-2) ?

The answer to taylor ln(3x-2) is 3(x-1)-9/2 (x-1)^2+9(x-1)^3-81/4 (x-1)^4+243/5 (x-1)^5+\ldots

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taylor ln(3x-2)

taylor

ln (3 x - 2)

3 (x - 1) - \frac{9}{2} (x - 1)^{2} + 9 (x - 1)^{3} - \frac{81}{4} (x - 1)^{4} + \frac{243}{5} (x - 1)^{5} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{3}{1 !} (x - 1) + \frac{- 9}{2 !} (x - 1)^{2} + \frac{54}{3 !} (x - 1)^{3} + \frac{- 486}{4 !} (x - 1)^{4} + \frac{5832}{5 !} (x - 1)^{5} + \dots

Refine

= 3 (x - 1) - \frac{9}{2} (x - 1)^{2} + 9 (x - 1)^{3} - \frac{81}{4} (x - 1)^{4} + \frac{243}{5} (x - 1)^{5} + \dots

\int \frac{3}{x} d x

ln (\frac{4 x - 4}{5 x + 9})

x y^{^{'}} - 3 y = 6

\frac{\partial}{\partial x} (e^{x^{2} + 2 y})

y = 10 x, y = x^{2}

What is taylor ln(3x-2) ?
The answer to taylor ln(3x-2) is 3(x-1)-9/2 (x-1)^2+9(x-1)^3-81/4 (x-1)^4+243/5 (x-1)^5+\ldots