What is taylor ln(7-3x) ?

The answer to taylor ln(7-3x) is ln(7)-3/7 x-9/98 x^2-9/343 x^3-81/9604 x^4+\ldots

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taylor ln(7-3x)

taylor

ln (7 - 3 x)

ln (7) - \frac{3}{7} x - \frac{9}{98} x^{2} - \frac{9}{343} x^{3} - \frac{81}{9604} x^{4} + \dots

Solution steps

Apply the Taylor Formula

= ln (7) + \frac{\frac{d}{d x} ( ln ( 7 - 3 x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( ln ( 7 - 3 x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ln ( 7 - 3 x ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= ln (7) + \frac{- \frac{3}{7}}{1 !} x + \frac{- \frac{9}{49}}{2 !} x^{2} + \frac{- \frac{54}{343}}{3 !} x^{3} + \frac{- \frac{486}{2401}}{4 !} x^{4} + \dots

Refine

= ln (7) - \frac{3}{7} x - \frac{9}{98} x^{2} - \frac{9}{343} x^{3} - \frac{81}{9604} x^{4} + \dots

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What is taylor ln(7-3x) ?
The answer to taylor ln(7-3x) is ln(7)-3/7 x-9/98 x^2-9/343 x^3-81/9604 x^4+\ldots