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mamaluj [8]
3 years ago
7

Solve the equationlog4x=2

Mathematics
1 answer:
Inessa05 [86]3 years ago
4 0
Change it to exponential form:

log₄(x) = 2   ⇒   4² = x = 16

Final answer: 16
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Use Newton’s Method to find the solution to x^3+1=2x+3 use x_1=2 and find x_4 accurate to six decimal places. Hint use x^3-2x-2=
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Let f(x) = x^3 - 2x - 2. Then differentiating, we get

f'(x) = 3x^2 - 2

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The x-intercept for this approximation will be our next approximation for the root,

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Once more. Approximate f(x) at x_3.

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Then

\dfrac{6,889,342}{931,225}x - \dfrac{11,762,638,074}{898,632,125} = 0 \\\\ \implies x_4 = \dfrac{5,881,319,037}{3,324,107,515} \approx 1.769292663 \approx \boxed{1.769293}

Compare this to the actual root of f(x), which is approximately <u>1.76929</u>2354, matching up to the first 5 digits after the decimal place.

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