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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.

You might be interested in
Locate and plot √11 on a number line. Find a better approximation using decimals. 3.2×3.2= 3.4×3.4 = (Type integers or decimals.
ki77a [65]

Answer:

The point 'R' shows the irrational number √11 on the given number line and for better proximation using decimals, 3.2×3.2= 10.24; 3.4×3.4= 11.56

Step-by-step explanation:

It is given that we have to locate √11 on a number line, so for that we need to mark point 'O' on the number line as shown;

Now,

On the number line, point 'O' represent 0 and the point 'L' represents 3. Thus, we have OL = 3 units.

Now, we will construct LM = 1 unit, which will be perpendicular to the number line given;

=> OM = √10

Now, we will further construct MN = 1 unit, which will be perpendicular to OM;

=> ON² = OM² + MN²

=> ON = √OM² + MN²

=> √(10)² + (1)²

=> √10+1

=> √11

Furthermore, With O as the center and ON = √11 for the radius, we create an arc that crosses the number line at R resulting that line OR = √11 (radius).

Therefore, the point 'R' shows the irrational number √11 on the given number line.

For better proximation using decimals, the answers are:

3.2 × 3.2 = 10.24

3.4 × 3.4 = 11.56

<u>To know more about representation on number line, click here</u>:

brainly.com/question/13425491

#SPJ10

8 0
2 years ago
How to solve this equation 2(f+3)+4f=6+6f?
Tresset [83]
2f+6+4f=6+6f
6f+6-6=6-6+6f
6f=6f
This means f can equal any number which we call mathematically infinite solution or infinitely many solutions
5 0
3 years ago
Read 2 more answers
Justin is paid $7.00 an hour and also earns a 20% commission on any sales he makes. In one week, if he worked 40 hours and had $
nignag [31]

Answer:

380

Step-by-step explanation:

7 x 40 = 280 + C = 380

C = Commision

500 x .2 = 100

C = 100

6 0
3 years ago
What is the y-intercept of the function, represented by the table of values
AleksandrR [38]

Answer:

9

Step-by-step explanation:

The table is given below

\left|\begin{array}{c|cc}x&y\\--&--\\-2&15\\1&6\\2&3\\4&-3\\7&-12\end{array}\right|

We can see that the table represents a linear function since by checking its slope.

Using:

  1. Points (-2,15) and (1,6)
  2. Points (1,6) and (2,3)

Slope =\dfrac{6-15}{1-(-2)} =\dfrac{3-6}{2-1}=-3

Therefore, the values represent a linear function.

A linear equation is of the form y=mx+b

Therefore:

y=-3x+b

Using the points (7,-12)

-12=-3(7)+b\\-12=-21+b\\b=-12+21\\b=9

Therefore, the y-intercept of the function, represented by the table of values is 9.

6 0
3 years ago
Domain and range of the function f(x)= 7x^5<br> PLEASE HELP I LITERALLY CANT DO IT
sineoko [7]

Answer:

Domain: all real numbers

Range: all real numbers

Step-by-step explanation:

The domain is all x values, and the range is all y values.

<u><em>Domain:</em></u>

The domain is all real numbers except where the slope is undefined (a vertical line). In this case, no number makes the expression undefined, so the domain is:

all real numbers

<u><em>Interval notation:</em></u><em>  </em>(-∞,∞)

all negative numbers and positive numbers (all real numbers)

<em><u>Set-Builder Notation:</u></em> {x | x ∈ R }

<em><u>Range:</u></em>

The range is the set of all valid values. Graph the line and check. Since all values of y are valid, the range is:

all real numbers

<u><em>Interval notation:</em></u><em>  </em>(-∞,∞)

all negative numbers and positive numbers (all real numbers)

<em><u>Set-Builder Notation:</u></em> {x | x ∈ R }

:Done

3 0
2 years ago
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