All categories

3 years ago

PLEASE HELP! WILL MARK AND GIVE POINTS.

Mathematics

1 answer:

marshall27 [118]3 years ago

6 0

Answer:

im not sure but i think it might be d

Step-by-step explanation:

You might be interested in

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

earnstyle [38]

Answer:

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

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 $a$ and $b$ 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 $x$ :

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

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

7 0

3 years ago

Find z. Just write the number. Answer should be a whole number. PLS HELP DUE IN 10 MINS WILL GIVE BRAINLIST

Delicious77 [7]

Answer:

square root of 338 or 18.38

Step-by-step explanation:

since a² and b² are equal, you would do 13² plus 13² then add those and you end up with 338. then you find the square root of 338 which is 18.38477631, or 18.38

5 0

3 years ago

What is the product of -3 and 5

weeeeeb [17]

Answer:

45 is the correct answer

6 0

3 years ago

Read 2 more answers

What is the surface area of the box if it is scaled up by a factor of 10? The surface area is 84 square inches.

inn [45]

Answer:

A for a box, the surface area is given by:

6l², where l is the length of one side.

If the side is increased 10 times,

6(10l)²

=100 x6l²

The surface area increases 100 times. Thus, the new surface area is

272 * 100

= 27,200 sq in

Step-by-step explanation:

7 0

3 years ago

Harry needs to build a fence around his garden, but first he must figure out the dimensions of his garden. The length of his rec

Lana71 [14]

First, we know L and W are the same number. The in the end the Length is 6 more, therefore we add 6. The equations begins as so
2x+6=27
-6
2x=21
/2
x=10.5
+6
Therefore the Width =10.5 M
The Length = 16.5 M

6 0

3 years ago