Question

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

Answer 1

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.

Answer 2

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