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sineoko [7]
2 years ago
6

Find 2^x=4x, find x ​

Mathematics
1 answer:
Sav [38]2 years ago
7 0

Whatever... I'll try to solve the first two problems.

2^x=4x\\4x=e^{\ln 2^x}\\4x=e^{x\ln 2}\\\dfrac{1}{4x}=e^{-x \ln 2}\\-\dfrac{\ln 2}{4}=-x\ln 2e^{-x \ln 2}\\-x\ln 2=W\left(-\dfrac{\ln 2}{4}\right)\\x=-\dfrac{W\left(-\dfrac{\ln 2}{4}\right)}{\ln 2}

1.

x=\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5\ldots}}}}}}\qquad\left( x\geq0\right)\\\\x=\sqrt{13+\sqrt{5+x}}\\\\x^2=13+\sqrt{5+x}\\\sqrt{5+x}=x^2-13\\\\D:5+x\geq0 \wedge x^2-13\geq 0\wedge x\geq 0\\D:x\geq-5 \wedge x^2\geq13\wedge x\geq 0\\D:x\geq \sqrt{13} \vee x\leq-\sqrt{13}\wedge x\geq0 \\D:x\in[\sqrt{13},\infty)\\\\ 5+x=x^4-26x^2+169\\x^4-26x^2-x+164=0\\\vdots\\(x - 4) (x^3 + 4 x^2 - 10 x - 41) = 0\\x-4=0\\x=4

One solution is x=4, and 4\in D, therefore\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5\ldots}}}}}}=4.

We can ignore other possible solutions of the polynomial equation, because the expression can not be equal to two different values simultaneously.

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The slope is \frac{3}{2}

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Step-by-step explanation:

The form of the equation that passes through two points (x1, y1) and (x2, y2) is y = m x + b, where

  • m is the slope of the line whose rule is m=\frac{y2-y1}{x2-x1}
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Let us solve the question:

Choose any two-point from the table

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∴ m = \frac{3}{2}

∴ The slope is \frac{3}{2}

→ Substitute its value in the form of the equation above

∴ y = \frac{3}{2} x + b

→ To find b substitute x and y by x1 and y1

∴ 12 = \frac{3}{2} (2) + b

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3 years ago
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