Write this number in standard form.

Intersection point of Y=logx and y=1/2log(x+1)

GalinKa [24]

Answer:

The intersection is $(\frac{1+\sqrt{5}}{2},\log(\frac{1+\sqrt{5}}{2})$ .

The Problem:

What is the intersection point of $y=\log(x)$ and $y=\frac{1}{2}\log(x+1)$ ?

Step-by-step explanation:

To find the intersection of $y=\log(x)$ and $y=\frac{1}{2}\log(x+1)$ , we will need to find when they have a common point; when their $x$ and $y$ are the same.

Let's start with setting the $y$ 's equal to find those $x$ 's for which the $y$ 's are the same.

$\log(x)=\frac{1}{2}\log(x+1)$

By power rule:

$\log(x)=\log((x+1)^\frac{1}{2})$

Since $\log(u)=\log(v)$ implies $u=v$ :

$x=(x+1)^\frac{1}{2}$

Squaring both sides to get rid of the fraction exponent:

$x^2=x+1$

This is a quadratic equation.

Subtract $(x+1)$ on both sides:

$x^2-(x+1)=0$

$x^2-x-1=0$

Comparing this to $ax^2+bx+c=0$ we see the following:

$a=1$

$b=-1$

$c=-1$

Let's plug them into the quadratic formula:

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{1 \pm \sqrt{(-1)^2-4(1)(-1)}}{2(1)}$

$x=\frac{1 \pm \sqrt{1+4}}{2}$

$x=\frac{1 \pm \sqrt{5}}{2}$

So we have the solutions to the quadratic equation are:

$x=\frac{1+\sqrt{5}}{2}$ or $x=\frac{1-\sqrt{5}}{2}$ .

The second solution definitely gives at least one of the logarithm equation problems.

Example: $\log(x)$ has problems when $x \le 0$ and so the second solution is a problem.

So the $x$ where the equations intersect is at $x=\frac{1+\sqrt{5}}{2}$ .

Let's find the $y$ -coordinate.

You may use either equation.

I choose $y=\log(x)$ .

$y=\log(\frac{1+\sqrt{5}}{2})$

The intersection is $(\frac{1+\sqrt{5}}{2},\log(\frac{1+\sqrt{5}}{2})$ .

6 0

3 years ago

Hey can you please help me posted picture of question

erma4kov [3.2K]

Selecting this function: F(x)= x^4-x^2+3

Graph using these selected points:
Rises to the left and rises to the right
x y
-1 3
0 3
1 3
2 15
3 75

After assigning values for x and y, plot the graph:
See attached picture for the graph.

We can now conclude that for the given graph, the equation of F(x) is equal to x^4-x^2+3 which is letter D. F(x)= x^4-x^2+3

3 0

4 years ago

Enita is factoring the expression 32 a b minus 8 b. She determines the GCF and writes the factored expression as 8 b (4 a minus

sattari [20]

This shows that the greatest common factor is 8, Hence Venita's error is that she incorrectly determined the GCF.

<h3>Greatest common factor</h3>

Given the following expression

32ab - 8

Find the factors of each terms

32ab = 8 * 4. * a * b

8 = 8 * 1

Since 8 is common to both factors, hence

32ab - 8 = 8(4ab -1)

This shows that the greatest common factor is 8, Hence Venita's error is that she incorrectly determined the GCF.

Learn more on GCF here; brainly.com/question/219464

#SPJ1

8 0

2 years ago

What is the least common multiple of the two denominators?

rusak2 [61]

Answer:

32

Step-by-step explanation:

32 × 1 = 32

8 × 4 = 32

Therefore, the LCM is 32

8 0

3 years ago

What’s the answer to this plssss??

Murljashka [212]

I ain't gonna explain how I got to this cuz I'm quite tired rn but trust me the answer is 2c²

4 0

3 years ago

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