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umka2103 [35]
3 years ago
6

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

Mathematics
1 answer:
faust18 [17]3 years ago
5 0
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.
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Answer:

14a+35

Step-by-step explanation:

7×2a=14a

7×5=35

=14a+25

3 0
3 years ago
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The population of a town was 7652 in 2016. The population grows at a rate of 1.6% annually.
Serggg [28]

Answer:

(A) The population's growth rate in equation form is y = (0.016t * 7652) + 7652

(B)  y = (0.016t * 7652) + 7652 =

y = (0.016(8) * 7652) + 7652 =

y = (0.128 * 7652) + 7652 =

y = 979.456 + 7652 =

y = 8631.456 (Or About) 8631

Step-by-step explanation:

(A) Y = the total population of the town. 0.016 is 1.6% just in its original form. T = the year in which were trying to find the town's total population. 7652 is the total population of the town in 2016. With this information, the equation reads, The total population of the town (Y) is equal to 16% (0.016) of the current year's population (T) added to 2016's population of 7652. (This last sentence can also be read what is 1.6% of the towns population in the year were trying to find. Because the population is always growing, 1.6% gets multiplied as to scale with the total population in year T)

(B) We just substitute (T) for 2024, or 8 years after 2016 (2024-2016) and simplify the equation we made.

7 0
3 years ago
Help me please thanks​
horrorfan [7]

Answer:

325m = c

Step-by-step explanation:

Each meeting room has 325 chairs.

Since we don't know how many meeting rooms there are, the number is replaced with the variable, m.

An equation is a problem with an equals sign so you need to put what it would equal.

Since you don't know how many meeting rooms there are you use the variable, c which represents the total number of chairs.

8 0
2 years ago
Brad's dinner bill, including a 16% tip, is $10.44.
Gnoma [55]

Answer:

<h2>£8.77</h2>

Step-by-step explanation:

100 - 16 = 84

84 / 100 = 0.84

10.44 x 0.84

=8.77

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2 years ago
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Solve for y.<br> -5y = 60<br> Enter your answer in the box <br><br><br> Y=
Airida [17]

Answer:

The answer is negative 12

Step-by-step explanation:

- 5y = 60

\frac{ - 5y}{ - 5}  =  \frac{60}{ -5}

y =  - 12

5 0
2 years ago
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