Answer:
x=5
Step-by-step explanation:
Well all i did was guess a random number from 1-10 so I could see what numbers make the equation bigger than -18 and the fist thing I guessed was 5 so this is what I did
8-6*5=-22
And them I said let me see if any multiples equal -18 so I went to for and did this
8-6*4=-16
That's when I guessed the answer if i looked at the sign correctly!
Answer:
See Explanation.
General Formulas and Concepts:
<u>Pre-Algebra</u>
<u>Algebra II</u>
- Log/Ln Property:
![ln(\frac{a}{b} ) = ln(a) - ln(b)](https://tex.z-dn.net/?f=ln%28%5Cfrac%7Ba%7D%7Bb%7D%20%29%20%3D%20ln%28a%29%20-%20ln%28b%29)
<u>Calculus</u>
Derivatives
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Chain Rule: ![\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28g%28x%29%29%5D%20%3Df%27%28g%28x%29%29%20%5Ccdot%20g%27%28x%29)
Derivative of Ln: ![\frac{d}{dx} [ln(u)] = \frac{u'}{u}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%20%5Bln%28u%29%5D%20%3D%20%5Cfrac%7Bu%27%7D%7Bu%7D)
Step-by-step explanation:
<u>Step 1: Define</u>
![ln(\frac{2x-1}{x-1} )=t](https://tex.z-dn.net/?f=ln%28%5Cfrac%7B2x-1%7D%7Bx-1%7D%20%29%3Dt)
<u>Step 2: Differentiate</u>
- Rewrite:
![t = ln(\frac{2x-1}{x-1})](https://tex.z-dn.net/?f=t%20%3D%20ln%28%5Cfrac%7B2x-1%7D%7Bx-1%7D%29)
- Rewrite [Ln Properties]:
![t = ln(2x-1) - ln(x - 1)](https://tex.z-dn.net/?f=t%20%3D%20ln%282x-1%29%20-%20ln%28x%20-%201%29)
- Differentiate [Ln/Chain Rule/Basic Power Rule]:
![\frac{dt}{dx} = \frac{1}{2x-1} \cdot 2 - \frac{1}{x-1} \cdot 1](https://tex.z-dn.net/?f=%5Cfrac%7Bdt%7D%7Bdx%7D%20%3D%20%5Cfrac%7B1%7D%7B2x-1%7D%20%5Ccdot%202%20-%20%5Cfrac%7B1%7D%7Bx-1%7D%20%5Ccdot%201)
- Simplify:
![\frac{dt}{dx} = \frac{2}{2x-1} - \frac{1}{x-1}](https://tex.z-dn.net/?f=%5Cfrac%7Bdt%7D%7Bdx%7D%20%3D%20%5Cfrac%7B2%7D%7B2x-1%7D%20-%20%5Cfrac%7B1%7D%7Bx-1%7D)
- Rewrite:
![\frac{dt}{dx} = \frac{2(x-1)}{(2x-1)(x-1)} - \frac{2x-1}{(2x-1)(x-1)}](https://tex.z-dn.net/?f=%5Cfrac%7Bdt%7D%7Bdx%7D%20%3D%20%5Cfrac%7B2%28x-1%29%7D%7B%282x-1%29%28x-1%29%7D%20-%20%5Cfrac%7B2x-1%7D%7B%282x-1%29%28x-1%29%7D)
- Combine:
![\frac{dt}{dx} = \frac{-1}{(2x-1)(x-1)}](https://tex.z-dn.net/?f=%5Cfrac%7Bdt%7D%7Bdx%7D%20%3D%20%5Cfrac%7B-1%7D%7B%282x-1%29%28x-1%29%7D)
- Reciprocate:
![\frac{dx}{dt} = -(2x-1)(x-1)](https://tex.z-dn.net/?f=%5Cfrac%7Bdx%7D%7Bdt%7D%20%3D%20-%282x-1%29%28x-1%29)
- Distribute:
![\frac{dx}{dt} = (1-2x)(x-1)](https://tex.z-dn.net/?f=%5Cfrac%7Bdx%7D%7Bdt%7D%20%3D%20%281-2x%29%28x-1%29)
You have sqrt(8), sqrt(18), and sqrt(2).
You need to simplify the radicals.
sqrt(2) is already simplified.
For both sqrt(8) and sqrt(18), you need to factor out the greatest perfect square.
8 = 4 * 2
You can take the square root of 4 and put it outside the root.
18 = 9 * 2
You can take the square root of 9 and put it outside the root.
![5 \sqrt{8} - \sqrt{18} -2 \sqrt{2} =](https://tex.z-dn.net/?f=%205%20%5Csqrt%7B8%7D%20-%20%5Csqrt%7B18%7D%20-2%20%5Csqrt%7B2%7D%20%3D%20)
![= 5 \sqrt{4 \times 2} - \sqrt{9 \times 2} -2 \sqrt{2}](https://tex.z-dn.net/?f=%3D%205%20%5Csqrt%7B4%20%5Ctimes%202%7D%20-%20%5Csqrt%7B9%20%5Ctimes%202%7D%20-2%20%5Csqrt%7B2%7D%20)
![= 5 \times 2\sqrt{2} - 3 \sqrt{2} -2 \sqrt{2}](https://tex.z-dn.net/?f=%3D%205%20%5Ctimes%202%5Csqrt%7B2%7D%20-%203%20%5Csqrt%7B2%7D%20-2%20%5Csqrt%7B2%7D%20)
![= 10\sqrt{2} - 3 \sqrt{2} -2 \sqrt{2}](https://tex.z-dn.net/?f=%3D%2010%5Csqrt%7B2%7D%20-%203%20%5Csqrt%7B2%7D%20-2%20%5Csqrt%7B2%7D%20)
Answer:
0.25 or 1/4
Step-by-step explanation: