If there are 4 prizes of every 9 boxes how many prizes are in 54 boxes

What are the potential solutions of log4x+log4(x+6)=2?

lions [1.4K]

The potential solutions of $log_4x+log_4(x+6)=2$ are 2 and -8.

<h3>Properties of Logarithms</h3>

From the properties of logarithms, you can rewrite logarithmic expressions.

The main properties are:

Product Rule for Logarithms - $log_{b}(a*c)=log_{b}a+log_{b}c$
Quotient Rule for Logarithms - $log_{b}(\frac{a}{c} )=log_{b}a-log_{b}c$
Power Rule for Logarithms - $log_{b}(a^c)=c*log_{b}a$

The exercise asks the potential solutions for $log_4x+log_4(x+6)=2$ . In this expression you can apply the Product Rule for Logarithms.

$log_4x+log_4(x+6)=2\\ \\ x*(x+6)=4^2\\ \\ x^2+6x=16\\ \\ x^2+6x-16=0$

Now you should solve the quadratic equation.

Δ= $b^2-4ac=36-4*1*(-16)=36+64=100$ . Thus, x will be $x_{1,\:2}=\frac{-6\pm \:\sqrt{100} }{2\cdot \:1}=\frac{-6\pm \:10}{2}$ . Then:

$x_1=\frac{-6+10}{2}=\frac{4}{2} =2\\ \\ \:x_2=\frac{-6-10}{2}=\frac{-16}{2} =-8$

The potential solutions are 2 and -8.

Read more about the properties of logarithms here:

brainly.com/question/14868849

4 0

2 years ago

The data set shown below represents the number of times some families went out for dinner the previous week. 4, 2, 2, 0, 1, 6, 3

Mkey [24]

Dot plots are used to represent data using dots

The true statements about the dataset are:

The range of the number line should be 0 to 7 to represent the frequency.
Four families said they ate out twice the previous week.
One family said they ate out 5 times the previous week

The dataset is given as:

4, 2, 2, 0, 1, 6, 3, 2, 5, 1, 2, 4, 0, 1

Rearrange in ascending order

0, 0, 1, 1, 2, 2, 2, 2, 4, 4, 5, 6

Represent as a frequency table

Data Frequency

0 2

1 2

2 4

3 0

4 2

5 1

6 1

See attachment for the dot plot

From the attachment, we can see that:

4 has a frequency of 2
5 has a frequency of 1

Also, the range on the dot plot can be 0 to 7, because it covers the given dataset

Hence, the true statements are: (a), (b) and (c)

Read more about dot plots at:

brainly.com/question/21862696

7 0

3 years ago

Read 2 more answers

Tom counted the number of cards in his collection for 10 weeks. By week 5, he had collected 12 cards. This graph shows this info

Karolina [17]

Answer:

i think it would be 17

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

How do I solve for this

Anon25 [30]

Answer: for 90 degrees it will be 1

for 180 degrees it will be $\sqrt{2}$ /2

Step-by-step explanation:

7 0

3 years ago

The current value of a baseball card is 60 times its original value v

jeka94

60v = $15

60v/60 = $15/60

v = 0.25

The original value of the baseball card is $0.25

5 0

3 years ago