What is maclaurin ln(2-3x) ?

The answer to maclaurin ln(2-3x) is ln(2)-3/2 x-9/8 x^2-9/8 x^3-81/64 x^4+\ldots

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maclaurin ln(2-3x)

maclaurin

ln (2 - 3 x)

ln (2) - \frac{3}{2} x - \frac{9}{8} x^{2} - \frac{9}{8} x^{3} - \frac{81}{64} x^{4} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= ln (2) + \frac{- \frac{3}{2}}{1 !} x + \frac{- \frac{9}{4}}{2 !} x^{2} + \frac{- \frac{27}{4}}{3 !} x^{3} + \frac{- \frac{243}{8}}{4 !} x^{4} + \dots

Refine

= ln (2) - \frac{3}{2} x - \frac{9}{8} x^{2} - \frac{9}{8} x^{3} - \frac{81}{64} x^{4} + \dots

\frac{d y}{d x} = \frac{x sec ( \frac{y}{x} ) + y}{x}

\int sec (\frac{x}{2}) tan (\frac{x}{2}) d x

y = 2 5 - x^{2}

\int (x^{2} + 3)^{3} 2 x d x

\frac{\partial}{\partial x} (x^{5} y^{5})

What is maclaurin ln(2-3x) ?
The answer to maclaurin ln(2-3x) is ln(2)-3/2 x-9/8 x^2-9/8 x^3-81/64 x^4+\ldots