Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 9+10(3x-10)=2
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Equation (x-4)/(x-6)=2
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Equation -x+9=16
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Equation x^2-4x+13=0
- Express {x} in terms of y where:
- -9*x+12*y=16
- -10*x+8*y=2
- -16*x+18*y=9
- 4*x-1*y=12
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Identical expressions
- lg(2x+ one)- one = zero
- lg(2x plus 1) minus 1 equally 0
- lg(2x plus one) minus one equally zero
- lg2x+1-1=0
- lg(2x+1)-1=O
-
Similar expressions
- lg(2x+1)+1=0
- lg(2x-1)-1=0
lg(2x+1)-1=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\log{\left(2 x + 1 \right)} - 1 = 0$$
$$\log{\left(2 x + 1 \right)} = 1$$
This equation is of the form:
By definition log
then
$$2 x + 1 = e^{1^{-1}}$$
simplify
$$2 x + 1 = e$$
$$2 x = -1 + e$$
$$x = - \frac{1}{2} + \frac{e}{2}$$
$$\log{\left(2 x + 1 \right)} - 1 = 0$$
$$\log{\left(2 x + 1 \right)} = 1$$
This equation is of the form:
log(v)=p
By definition log
v=e^p
then
$$2 x + 1 = e^{1^{-1}}$$
simplify
$$2 x + 1 = e$$
$$2 x = -1 + e$$
$$x = - \frac{1}{2} + \frac{e}{2}$$
Sum and product of roots
[src]
sum
1 E - - + - 2 2
$$- \frac{1}{2} + \frac{e}{2}$$
=
1 E - - + - 2 2
$$- \frac{1}{2} + \frac{e}{2}$$
product
1 E - - + - 2 2
$$- \frac{1}{2} + \frac{e}{2}$$
=
1 E - - + - 2 2
$$- \frac{1}{2} + \frac{e}{2}$$
-1/2 + E/2