Mister Exam
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How to use it?
- Equation:
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Equation 3x^2=2x+x^3
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Equation 2*(-4*x^2/(x^2-4)+1+(x^2+4)*(4*x^2/(x^2-4)-1)/(x^2-4))/(x^2-4)=0
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Equation 4(x+6)=x
- Express {x} in terms of y where:
- 3*x-9*y=5
- -1*x+20*y=16
- -4*x+6*y=3
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- Derivative of:
-
ln|x|
- Integral of d{x}:
- ln|x|
-
Identical expressions
- |cos(x)|- one =ln|x|
- module of co sinus of e of (x)| minus 1 equally ln|x|
- module of co sinus of e of (x)| minus one equally ln|x|
- |cosx|-1=ln|x|
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Similar expressions
- ln(|x|)/2=-ln(|p-1|)+C
- |cos(x)|+1=ln|x|
- |cosx|-1=ln|x|
|cos(x)|-1=ln|x| equation
The teacher will be very surprised to see your correct solution 😉
The solution
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|cos(x)| - 1 = log(|x|)
$$\left|{\cos{\left(x \right)}}\right| - 1 = \log{\left(\left|{x}\right| \right)}$$
Detail solution
Given the equation
$$\left|{\cos{\left(x \right)}}\right| - 1 = \log{\left(\left|{x}\right| \right)}$$
transform
$$- \log{\left(\left|{x}\right| \right)} + \left|{\cos{\left(x \right)}}\right| - 1 = 0$$
$$\left(\left|{\cos{\left(x \right)}}\right| - 1\right) - \log{\left(\left|{x}\right| \right)} = 0$$
Do replacement
$$w = \left|{x}\right|$$
Given the equation
$$- \log{\left(w \right)} + \left|{\cos{\left(x \right)}}\right| - 1 = 0$$
$$- \log{\left(w \right)} = 1 - \left|{\cos{\left(x \right)}}\right|$$
Let's divide both parts of the equation by the multiplier of log =-1
$$\log{\left(w \right)} = \left|{\cos{\left(x \right)}}\right| - 1$$
This equation is of the form:
By definition log
then
$$w = e^{\frac{1 - \left|{\cos{\left(x \right)}}\right|}{-1}}$$
simplify
$$w = e^{\left|{\cos{\left(x \right)}}\right| - 1}$$
do backward replacement
$$\left|{x}\right| = w$$
substitute w:
$$\left|{\cos{\left(x \right)}}\right| - 1 = \log{\left(\left|{x}\right| \right)}$$
transform
$$- \log{\left(\left|{x}\right| \right)} + \left|{\cos{\left(x \right)}}\right| - 1 = 0$$
$$\left(\left|{\cos{\left(x \right)}}\right| - 1\right) - \log{\left(\left|{x}\right| \right)} = 0$$
Do replacement
$$w = \left|{x}\right|$$
Given the equation
$$- \log{\left(w \right)} + \left|{\cos{\left(x \right)}}\right| - 1 = 0$$
$$- \log{\left(w \right)} = 1 - \left|{\cos{\left(x \right)}}\right|$$
Let's divide both parts of the equation by the multiplier of log =-1
$$\log{\left(w \right)} = \left|{\cos{\left(x \right)}}\right| - 1$$
This equation is of the form:
log(v)=p
By definition log
v=e^p
then
$$w = e^{\frac{1 - \left|{\cos{\left(x \right)}}\right|}{-1}}$$
simplify
$$w = e^{\left|{\cos{\left(x \right)}}\right| - 1}$$
do backward replacement
$$\left|{x}\right| = w$$
substitute w: