Mister Exam
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Identical expressions
- log2x2= one
- logarithm of 2x2 equally 1
- logarithm of 2x2 equally one
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Similar expressions
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log2x2=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$2 \log{\left(2 x \right)} = 1$$
$$2 \log{\left(2 x \right)} = 1$$
Let's divide both parts of the equation by the multiplier of log =2
$$\log{\left(2 x \right)} = \frac{1}{2}$$
This equation is of the form:
By definition log
then
$$2 x = e^{\frac{1}{2}}$$
simplify
$$2 x = e^{\frac{1}{2}}$$
$$x = \frac{e^{\frac{1}{2}}}{2}$$
$$2 \log{\left(2 x \right)} = 1$$
$$2 \log{\left(2 x \right)} = 1$$
Let's divide both parts of the equation by the multiplier of log =2
$$\log{\left(2 x \right)} = \frac{1}{2}$$
This equation is of the form:
log(v)=p
By definition log
v=e^p
then
$$2 x = e^{\frac{1}{2}}$$
simplify
$$2 x = e^{\frac{1}{2}}$$
$$x = \frac{e^{\frac{1}{2}}}{2}$$
Sum and product of roots
[src]
sum
1/2 e ---- 2
$$\frac{e^{\frac{1}{2}}}{2}$$
=
1/2 e ---- 2
$$\frac{e^{\frac{1}{2}}}{2}$$
product
1/2 e ---- 2
$$\frac{e^{\frac{1}{2}}}{2}$$
=
1/2 e ---- 2
$$\frac{e^{\frac{1}{2}}}{2}$$
exp(1/2)/2