E^2x - e^x - 6 = 0 (solve exponential equation(

Mathematics

1 answer:

krek1111 [17]3 years ago

6 0

Let's assume, $e^x = y.$

Hence, the given equation can be written as:

y² - y - 6 = 0

Next step is to factor the trinomial. For that, break down the constant -6 into two multiples so that their addition will result the coefficient of y =-1.

So, 6 = -3* 2

And sum of -3 and 2 will give -1.

Therefore, we can replace -y with -3y + 2y. So,

y² - 3y + 2y - 6 =0

(y² - 3y) + (2y - 6) =0 Make the group of terms.

y(y - 3)+ 2(y -3) =0 Take out the common factor from each group.

(y - 3 ) (y + 2) = 0 Take out the common factor (y - 3).

So, y - 3 = 0 and y + 2 =0 Equate both factor equal to 0.

Hence, y = 3 and -2.

So, $e^x = 3 , e^x=-2$

$lne^x =ln 3 , lne^x=ln(-2)$ Taking ln to each sides.

So, x = ln 3

But ln (-2) is not defined.

So, x = ln (3) is the real solution of the given equation.

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In a viral pool test it is known that in a group of five (5) people, exactly one (1) will test positive. If they are tested one

creativ13 [48]

Answer:

$\frac{4}{20}$ or 0.2 or 20%

Step-by-step explanation:

For only two tests to be needed this means that the first test would need to come back as negative and the second test would be to come back as positive. Therefore, to find the probability of this happening we first need to find the probability of each individual test and multiply them together.

The first test needs to come back negative, there are four negative individuals out of the total 5 that are in the group. Therefore, the probability of the first test is 4/5.

Now we remove the individual that has just been tested and we are left with 4 total subjects in the group, of which only 1 is positive. Therefore, the probability of the second test is 1/4. Now we need to multiply these two probabilities together to get the probability of only needing two tests.

$\frac{4 * 1}{5 * 4} = \frac{4}{20}$ or 0.2 or 20%