What is a solution to the problem x^3 + ln(x+1) =8?

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Ashwini Raut

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The function f(x)=x3+ln(x+1) is defined over (−1,∞) . The limit at −1 is −∞ , the limit at ∞ is ∞ . The derivative is f′(x)=3x2+1x+1>0 so you know that the function is strictly increasing. Therefore the given equation has a single solution....
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The function f(x)=x3+ln(x+1) is defined over (−1,∞) . The limit at −1 is −∞ , the limit at ∞ is ∞ . The derivative is f′(x)=3x2+1x+1>0 so you know that the function is strictly increasing. Therefore the given equation has a single solution. Since f(2)>8 and f(1)<8 , the solution is inside the interval (1,2) . You can determine an approximation with the desired accuracy with numerical methods. read less
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