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Information reference tables what is the solution set of the equation log4 (x2 + 3x) − log4 (x + 5) = 1?

faust18 [17]

Use this property of logarithms:

$\log_b\left(\dfrac{x}{y}\right)=\log_b x-\log_b y$

Your equation transforms into:

$log_4\left(\dfrac{x^2+3x}{x+5}\right)=1$

Now, you have to apply the definition of a logarithm to express the equation in exponential form:

$\dfrac{x^2+3x}{x+5} = 4^1$

In case you don't remember, this is the definition of a logarithm:

$\log_b x = y \iff b^y = x$

The log is the exponent (y) you have to raise the base (b) to in order to get the power (x).

Finally, solve the rational equation:

$\dfrac{x^2+3x}{x+5} =4 \iff x^2+3x=4(x+5)$
$\iff x^2-x-20=0$
$\iff x=\dfrac{1\pm\sqrt{(-1)^2-4\cdot(-20)}}{2}= \left \{ {{5} \atop {-4}} \right.$

The correct answer is d.

5 0

3 years ago

When placed end to end, three red rods are 2 cm longer than than 2 blue rods. Three blue rods are 2 cm longer than four red rods

Oxana [17]

Answer:

Red = 10 cm, blue = 14 cm

Step-by-step explanation:

Let the length of each red rod be r and each blue rod be b

Then we have:

3r - 2b = 2
3b - 4r = 2

Multiply the first equation by 3 and the second one by 2:

9r - 6b = 6
6b - 8r = 4

Add the equations to eliminate one of variables:

9r - 8r = 6 + 4
r = 10 cm

Find the value of b:

3*10 -2b = 2
30 - 2 = 2b
2b = 28
b = 14 cm

5 0

3 years ago

Write a polynomial in standard form that represents the area of the shaded region.

Paladinen [302]

Answer:

Area of the smaller square is x * x, which is x^2

Area of the larger square is (x + 7)(x + 7), which is x^2 + 14x + 49

The area of the shaded area = Area of the larger square - Area of the smaller square

Area of the shaded region = x^2 + 14x + 49 - x^2

Area of the shaded region is 14x + 49.

7 0

2 years ago

Using the photo above:what is the surface area of the rectangular prism

Mandarinka [93]

Answer:

A=592

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Determine if the graph is a function then state the domain and range.

nignag [31]

<h3>Explanation</h3>

A function is a set of relation that doesn't have repetitive domain. If we want to know if a graph is function or not, we have to do the line test.

Line Test

Draw a vertical line. Make sure that a line passes through a graph.
See if a line intercepts a graph more than one point or just only one.

Result

If a line intercepts a graph more than one point, it is not a function.

However, if a line only intercepts a graph just one point, it is indeed a function.

The given graph from the question is a function because it passes line test.

Domain and Range

Domain is the set of all x-values, meaning we only focus on x-axis or x-value only.

Range is the set of all y-values. We only focus on y-value or y-axis for Range.

Determine Domain from Graph

We can simply say that the domain is from starting domain or x-coordinate point to end x-coordinate point. For example, if a graph starts at x = -4 and ends at x = 2, we can say that - 4<=x=2.

Determine Range from Graph

Similar to Domain except Range starts from the minimum value or point to the maximum point or value. For example if a graph starts at min point = 6 and max point = 9. We can say that 6<=y<=9.

From the graph, the domain starts from negative infinity to positive infinity. Meaning that x can be any numbers. Hence, the domain is set of all real numbers. For range, the minimum value is 0 and max value is positive infinity. Therefore we write y>=0.

<h3>Answer</h3>

 $\begin{cases} x \in \mathbb{R} \\ y \geqslant 0 \end{cases}$ 

Domain is set of all real numbers.

Range is greater or equal to 0.

8 0

2 years ago

U want free points?just answer this question:1+1​

U want free points?just answer this question:1+1