Name two numbers that are 14 units from 2 on the number line

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

2 years ago

F(40)=0.015(40)+56.53

Tems11 [23]

Answer:

F(40)=57.13

Step-by-step explanation:

0.015(40)=.6

.6+56.53=57.13

6 0

2 years ago

What is the mean of the distribution

nadezda [96]

the awnser is 799 by 983

Step-by-step explanation:

8 0

2 years ago

The length of a rectangle is five times its width. If the perimeter is at most 96 centimeters, what is the greatest possible val

Anvisha [2.4K]

Answer is in the attachment below.

7 0

3 years ago

Can I please have the answers.

Brums [2.3K]

Question 22.). Write the equation in Standard Form:

10y = 12x + 0.7

Identify: A, B, C

Standard Form for Linear Equation: Ax + By = C

10y = 12x + 0.7

The Standard Form of the solution is

Ax + By = C, Where, A ≥ 0

A and B, are Non- Zero numbers.

Therefore, Your answer, Letter Choice, (D), 120x - 100y = - 7, Where,

A = 120, B = - 100, and C = - 7

Question 24.). Described as, Inconsistent, Consistent, and Independent, Consistent, and Dependent, or None of These.

9x - 8y = 15, and 27x - 24y = 3

Solve:

9x - 8y = 15; 27x - 24y = 3

Steps: I will try to solve the system of equation:

9x - 8y = 15; 27x - 24y = 3

Step, Solve: 9x - 8y = 15 for x

9x - 8y + 8y = 15 + 8y

Add 8y to both sides:

9x = 8y + 15

9x/9 = 8y + 15/9 ( Divide both sides by 9):

x = 8/9y + 5/3

Step Substitute:

8/9y + 5/3 for X in 27x - 24y = 3

27x - 24y = 3

27 ( 8/9y + 5/3) - 24y = 3

45 = 3

Simplify Both sides of equation:

45 + - 45 = 3 + - 45 ( Add - 45, to both sides.):

0 = - 42

Therefore, No real Solutions, to both Equation.

Hence; 9x - 8y = 15; and 27x - 24 = 3, have No Real Solutions, and Therefore, They are, Answer Letter Choice, (B), Inconsistent.

Hope that helps!!! Sorry, I couldn't figure out Number (23.). : )

8 0

3 years ago