Mister Exam
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-2
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-2
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-2
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Identical expressions
- log two (x- three)=-2
- logarithm of 2(x minus 3) equally minus 2
- logarithm of two (x minus three) equally minus 2
- log2x-3=-2
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Similar expressions
- log2(x+3)=-2
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- x^3-(17/2)*x^2+20*x-(25/2)=0
log2(x-3)=-2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
log(x - 3) ---------- = -2 log(2)
$$\frac{\log{\left(x - 3 \right)}}{\log{\left(2 \right)}} = -2$$
Detail solution
Given the equation
$$\frac{\log{\left(x - 3 \right)}}{\log{\left(2 \right)}} = -2$$
$$\frac{\log{\left(x - 3 \right)}}{\log{\left(2 \right)}} = -2$$
Let's divide both parts of the equation by the multiplier of log =1/log(2)
$$\log{\left(x - 3 \right)} = - 2 \log{\left(2 \right)}$$
This equation is of the form:
By definition log
then
$$x - 3 = e^{- \frac{2}{\frac{1}{\log{\left(2 \right)}}}}$$
simplify
$$x - 3 = \frac{1}{4}$$
$$x = \frac{13}{4}$$
$$\frac{\log{\left(x - 3 \right)}}{\log{\left(2 \right)}} = -2$$
$$\frac{\log{\left(x - 3 \right)}}{\log{\left(2 \right)}} = -2$$
Let's divide both parts of the equation by the multiplier of log =1/log(2)
$$\log{\left(x - 3 \right)} = - 2 \log{\left(2 \right)}$$
This equation is of the form:
log(v)=p
By definition log
v=e^p
then
$$x - 3 = e^{- \frac{2}{\frac{1}{\log{\left(2 \right)}}}}$$
simplify
$$x - 3 = \frac{1}{4}$$
$$x = \frac{13}{4}$$
Sum and product of roots
[src]
sum
13/4
$$\frac{13}{4}$$
=
13/4
$$\frac{13}{4}$$
product
13/4
$$\frac{13}{4}$$
=
13/4
$$\frac{13}{4}$$
13/4