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motikmotik
3 years ago
10

SECTION B: LOGARITHMS A Question Three: Solve the equation log₂ (4x² - 9).- log₂ (2x + 3) = 3. Hint: (4x² - 9) is a difference o

f two squares.​
Mathematics
2 answers:
lorasvet [3.4K]3 years ago
5 0

Answer:

x = 11/2

Step-by-step explanation:

Use rules for logarithms to write it as a single log. Then use the hint to simplify further. Change it to exponential form to solve. See image.

Shalnov [3]3 years ago
3 0

Answer: 2x+3

Step-by-step explanation: Simplify   ———————

           2x - 3

Trying to factor as a Difference of Squares:

2.1      Factoring:  4x2 - 9

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  4  is the square of  2

Check : 9 is the square of 3

Check :  x2  is the square of  x1

Factorization is :       (2x + 3)  •  (2x - 3)

Canceling Out :

2.2    Cancel out  (2x - 3)  which appears on both sides of the fraction line.

Final result :

 2x + 3

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What is the value of n when 8n - 8 = 6n+ 6
777dan777 [17]
To solve for this, we need to get n by itself on one side, then solve from there.
Currently, our equation is 8n - 8 = 6n + 6.
Get n on one side, subtract 6n from both sides.
2n - 8 = 6
Add 8 to both sides.
2n = 14
Divide by 2 to get n.
n = 7.
I hope this helps!
4 0
4 years ago
A dietitian is interested in the average amount of time teenagers exercise per week. Based on previous studies, teenagers exerci
joja [24]

Answer:

The dietitian should conclude that there is no significant evidence to support the claim that the number of hours teenagers exercise per week has increased.

Step-by-step explanation:

H0 : μ = 6.5

H1 : μ > 6.5

The test statistic value = 3.30

The critical value > test statistic

The Decison region :

If; test statistic > critical value (Fail to reject H0)

If; test statistic < Critical value (Reject H0)

Given that the test statistic is > critical value ; then we fail to reject the null

Hence, the dietitian should conclude that there is no significant evidence to support the claim that the number of hours teenagers exercise per week has increased.

8 0
3 years ago
Ten times the smallest of three consecutive integers is 213 more than the sum of the other two integers. Find the integers.
mihalych1998 [28]

Answer:

27,28 and 29

Step-by-step explanation:

10*a = a+1+a+2+213

10a - 2a = 216

8a = 216

a = 27

27, 28, and 29

4 0
3 years ago
I am a 3 digit separated by commas in a multidigit number
Lana71 [14]
The comments are that they both are multidigits numbers
7 0
3 years ago
A conference will take place in a large hotel meeting room. The organizers of the conference have created a drawing for how to a
Tcecarenko [31]

Answer:

The actual length of the room is 40 feet

Step-by-step explanation:

Given

Scale = \frac{1}{2}\ inch : 12\ feet

Required

Determine the actual measurement of 3\frac{1}{3}\ inches

Represent the required actual measurement with x

i.e.

3\frac{1}{3}\ inches : x

And we have:

\frac{1}{2}\ inch : 12\ feet

3\frac{1}{3}\ inches : x

Cross Multiply

x * \frac{1}{2} = 12 * 3\frac{1}{3}

Convert fraction to improper fraction

x * \frac{1}{2} = 12 *\frac{10}{3}

\frac{x}{2} = \frac{120}{3}

\frac{x}{2} = 40

Multiply both sides by 2

x = 40 * 2

x = 80\ feet

<em>The actual length of the room is 40 feet</em>

8 0
3 years ago
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