Mister Exam
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How to use it?
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Identical expressions
- log(x- one ,5x)= two
- logarithm of (x minus 1,5x) equally 2
- logarithm of (x minus one ,5x) equally two
- logx-1,5x=2
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Similar expressions
- log(x+1,5x)=2
log(x-1,5x)=2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
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[src]
/ 3*x\ log|x - ---| = 2 \ 2 /
$$\log{\left(- \frac{3 x}{2} + x \right)} = 2$$
Detail solution
Given the equation
$$\log{\left(- \frac{3 x}{2} + x \right)} = 2$$
$$\log{\left(- \frac{x}{2} \right)} = 2$$
This equation is of the form:
By definition log
then
$$- \frac{x}{2} = e^{\frac{2}{1}}$$
simplify
$$- \frac{x}{2} = e^{2}$$
$$x = - 2 e^{2}$$
$$\log{\left(- \frac{3 x}{2} + x \right)} = 2$$
$$\log{\left(- \frac{x}{2} \right)} = 2$$
This equation is of the form:
log(v)=p
By definition log
v=e^p
then
$$- \frac{x}{2} = e^{\frac{2}{1}}$$
simplify
$$- \frac{x}{2} = e^{2}$$
$$x = - 2 e^{2}$$
Sum and product of roots
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sum
2 -2*e
$$- 2 e^{2}$$
=
2 -2*e
$$- 2 e^{2}$$
product
2 -2*e
$$- 2 e^{2}$$
=
2 -2*e
$$- 2 e^{2}$$
-2*exp(2)