Mathematics, 26.12.2020 14:00 coolstacie

Find x?
In 3x - In(x - 4) = ln(2x - 1) +ln3

Answers: 1

Show answers

Answers

Answer from: yazmincruz3766

$x = \displaystyle \frac{5 + \sqrt{17}}{2}$ .

Step-by-step explanation:

Because $3\, x$ is found in the input to a logarithm function in the original equation, it must be true that $3\, x 0$ . Therefore, x 0 .

Similarly, because (x - 4) and $(2\, x - 1)$ are two other inputs to the logarithm function in the original equation, they should also be positive. Therefore, x 4 .

Let and represent two positive numbers (that is: a 0 and b 0 .) The following are two properties of logarithm:

$\displaystyle \ln (a) + \ln(b) = \ln\left(a \cdot b\right)$ .

$\displaystyle \ln (a) - \ln(b) = \ln\left(\frac{a}{b}\right)$ .

Apply these two properties to rewrite the original equation.

Left-hand side of this equation:

$\begin{aligned}&\ln(3\, x) - \ln(x - 4)= \ln\left(\frac{3\, x}{x -4}\right)\end{aligned}$

Right-hand side of this equation:

$\ln(2\, x- 1) + \ln(3) = \ln\left(3 \left(2\, x - 1\right)\right)$ .

Equate these two expressions:

$\begin{aligned}\ln\left(\frac{3\, x}{x -4}\right) = \ln(3(2\, x - 1))\end{aligned}$ .

The natural logarithm function $\ln$ is one-to-one for all positive inputs. Therefore, for the equality $\begin{aligned}\ln\left(\frac{3\, x}{x -4}\right) = \ln(3(2\, x - 1))\end{aligned}$ to hold, the two inputs to the logarithm function have to be equal and positive. That is:

$\displaystyle \frac{3\ x}{x - 4} = 3\, (2\, x - 1)$ .

Simplify and solve this equation for :

$x^2 - 5\, x + 2 = 0$ .

There are two real (but not rational) solutions to this quadratic equation: $\displaystyle \frac{5 + \sqrt{17}}{2}$ and $\displaystyle \frac{5 - \sqrt{17}}{2}$ .

However, the second solution, $\displaystyle \frac{5 - \sqrt{17}}{2}$ , is not suitable. The reason is that if $x = \displaystyle \frac{5 - \sqrt{17}}{2}$ , then (x - 4) , one of the inputs to the logarithm function in the original equation, would be smaller than zero. That is not acceptable because the inputs to logarithm functions should be greater than zero.

The only solution that satisfies the requirements would be $\displaystyle \frac{5 + \sqrt{17}}{2}$ .

Therefore, $x = \displaystyle \frac{5 + \sqrt{17}}{2}$ .

Answer from: Quest

solution:

as, mean is defined as sum of all the observations divided by total number of observations.

and , median is mid value of the data whether arranged in ascending order or descending order.

consider, roadsters:

2,3,4,5,6,7,8,9

mean = $\frac{2+3+4+5+6+7+8+9}{8}=\frac{44}{8}=5.5$

also, median= $\frac{5+6}{2}=\frac{11}{2}=5.5$ , because number of observations is even, so median is mean of two mid values.

now, coming to bandits

2,3,4,5,6

mean = $\frac{2+3+4+5+6}{5}=\frac{20}{5}=4$

median = 4, as number of observations is odd.

so, roadsters has greater median as well mean than bandits.

→option a is true about the repairs performed on 2 types of cars:

bandits have lower median and mean than roadsters.

Answer from: Quest

the 3rd option is right

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 13:20

What additional information could be used to prove that δxyz ≅ δfeg using asa or aas? check all that apply. ∠z ≅ ∠g and xz ≅ fg ∠z ≅ ∠g and ∠y ≅ ∠e xz ≅ fg and zy ≅ ge xy ≅ ef and zy ≅ fg ∠z ≅ ∠g and xy ≅ fe

Answers: 2

Answer

Mathematics, 21.06.2019 15:50

Assemble the proof by dragging tiles to the statements and reasons column

Answers: 2

Answer

Mathematics, 21.06.2019 20:30

Ateacher brought a pack of 17 batteries . each calculator uses 3 batteries . how many calculator can the teacher fill with batteries

Answers: 2

Answer

Mathematics, 21.06.2019 23:50

Mariah is randomly choosing three books to read from the following: 5 mysteries, 7 biographies, and 8 science fiction novels. which of these statements are true? check all that apply. there are 20c3 possible ways to choose three books to read. there are 5c3 possible ways to choose three mysteries to read. there are 15c3 possible ways to choose three books that are not all mysteries. the probability that mariah will choose 3 mysteries can be expressed as . the probability that mariah will not choose all mysteries can be expressed as 1 −

Answers: 1

Answer

You know the right answer?

Find x?
In 3x - In(x - 4) = ln(2x - 1) +ln3...

Questions

Mathematics, 19.09.2019 07:10

Which answer describes the simpler problems that could be used to solve this story problem? tia paid a total of $10.66 for 2 boxes of cereal a...