Question

Find by Newton's method the root of the equation
xlog_(10 )x=4
near x=6 correct to 3 decimal places of digits.

Answer 1

Answer on Question #85780 – Math – Quantitative Methods

Question

Find by Newton's method the root of the equation

$$x \log_{- (10)} x = 4$$

near $x = 6$ correct to 3 decimal places of digits.

Solution

$$x \log_{10} x = 4 \rightarrow x \log_{10} x - 4 = 0 \rightarrow \frac{x \ln x}{\ln 10} - 4 = 0.$$

Newton's method: $x_{n+1} = x_n - \frac{x_n \ln x_n - 4 \ln 10}{\ln x_n + 1}$.

$$x_0 = 6.$$ $$x_1 = 5.4483.$$ $$x_2 = 5.4386.$$ $$x_3 = 5.4386.$$

So, $x = 5.4386$ is correct to 3 decimal places of digits.

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