All categories

3 years ago

Kim solved the equation below by graphing a system of equations. log base 2 (3x-1) = log base 4 (x+8)

Mathematics

2 answers:

kompoz [17]3 years ago

8 0

Answer:

solution is

$x=1.353,y=1.613$

Step-by-step explanation:

We are given equation as

$log_2(3x-1)=log_4(x+8)$

Firstly, we will find equations

First equation is

$y=log_2(3x-1)$

Second equation is

$y=log_4(x+8)$

now, we can draw graph

and then we can find intersection point

we can see that

intersection point is (1.353,1.613)

so, solution is

$x=1.353,y=1.613$

ExtremeBDS [4]3 years ago

7 0

Answer:

The solution to the given equation is at point (1.353, 1.613). Step-by-step explanation:

Given : Kim solved the equation below by graphing a system of equations.

$\log_2(3x-1)=\log_4(x+8)$

To find : What is the approximate solution to the equation?

Solution :

Let, $y_1=\log_2(3x-1)$

and $y_2=\log_4(x+8)$

Now, we plot these two equations.

The graph of $y_1=\log_2(3x-1)$ is shown with red line.

The graph of $y_2=\log_4(x+8)$ is shown with blue line.

The solution to this system will be their intersection point.

The intersection point of these graph is (1.353, 1.613)

Refer the attached graph below.

Therefore, The solution to the given equation is at point (1.353, 1.613).

You might be interested in

Use a proof by contradiction to show that the square root of 3 is national You may use the following fact: For any integer kirke

Ierofanga [76]

Answer:

1. Let us proof that √3 is an irrational number, using reductio ad absurdum. Assume that $\sqrt{3}=\frac{m}{n}$ where $m$ and $n$ are non negative integers, and the fraction $\frac{m}{n}$ is irreducible, i.e., the numbers $m$ and $n$ have no common factors.

Now, squaring the equality at the beginning we get that

$3=\frac{m^2}{n^2}$ (1)

which is equivalent to $3n^2=m^2$ . From this we can deduce that 3 divides the number $m^2$ , and necessarily 3 must divide $m$ . Thus, $m=3p$ , where $p$ is a non negative integer.

Substituting $m=3p$ into (1), we get

$3= \frac{9p^2}{n^2}$

which is equivalent to

$n^2=3p^2$ .

Thus, 3 divides $n^2$ and necessarily 3 must divide $n$ . Hence, $n=3q$ where $q$ is a non negative integer.

Notice that

$\frac{m}{n} = \frac{3p}{3q} = \frac{p}{q}$ .

The above equality means that the fraction $\frac{m}{n}$ is reducible, what contradicts our initial assumption. So, $\sqrt{3}$ is irrational.

2. Let us prove now that the multiplication of an integer and a rational number is a rational number. So, $r\in\mathbb{Q}$ , which is equivalent to say that $r=\frac{m}{n}$ where $m$ and $n$ are non negative integers. Also, assume that $k\in\mathbb{Z}$ . So, we want to prove that $k\cdot r\in\mathbb{Z}$ . Recall that an integer $k$ can be written as

$k=\frac{k}{1}$ .

Then,

$k\cdot r = \frac{k}{1}\frac{m}{n} = \frac{mk}{n}$ .

Notice that the product $mk$ is an integer. Thus, the fraction $\frac{mk}{n}$ is a rational number. Therefore, $k\cdot r\in\mathbb{Q}$ .

3. Let us prove by reductio ad absurdum that the sum of a rational number and an irrational number is an irrational number. So, we have $x$ is irrational and $p\in\mathbb{Q}$ .

Write $q=x+p$ and let us suppose that $q$ is a rational number. So, we get that

$x=q-p$ .

But the subtraction or addition of two rational numbers is rational too. Then, the number $x$ must be rational too, which is a clear contradiction with our hypothesis. Therefore, $x+p$ is irrational.

7 0

4 years ago

Without solving what can you tell about the solution

nlexa [21]

Answer:

n has to be negative

8 0

3 years ago

PLEASE I BEG ANYONE TO HELP ME ANWER THIS MATH QUESTION!!!

Rus_ich [418]

Its the first one.
Explanation: The equation equals x=3/5 and so does the first one.

5 0

3 years ago

R+3.2=6.1 What is the value of r? Show work

ankoles [38]

Hello,

The answer is 2.9.

Reason:

Solve this two ways:

1. You could be just regularly solving the question but subtracting 6.1 to 3.2.

6.1-3.2=2.9

2. Or you could be solving variable.

Subtract 3.2 on both sides:

6.1-3.2=2.9

r=2.9

If you need anymore help feel free to ask me!

Hope this helps!

~Nonportrit

4 0

3 years ago

Read 2 more answers

A fruit stand has to decide what to charge for their produce. They need $10 for 4 apples and 4 oranges.

Anestetic [448]

A works because 1 • 4 + 1.5 • 4 = 10 and 1 • 6 + 1.5 • 6 = 15

5 0

3 years ago