Question

Match each equation with its solution.

Answer 1

1. x = -2 , 3

2. x = - 1, 5

3. -1, 6/5

4. - 0/3, 1.3

Explanation:

1.

`ln(x+5)=ln(x-1)+ln(x+1)\\\\x+ 5 = (x-1)(x+1)\\\\x + 5 = x^2 - 1\\\\x^2 - x - 6 = 0 \\\\x^2 - 3 x + 2 x - 6 =0 \\\\x(x-3)+2(x-3)=0\\\\x = -2 and 3`

2.

`e^{x^(2)}=e^(4x +5)\\\\x^2 - 4x - 5 = 0 \\\\x^2 - 5x + x - 5 = 0 \\\\x (x-5)+1 (x-5)=0\\\\x = -1 and 5`

3.

`log_(4)(5x^2 +2)=log_(4)(x +8)\\\\5x^2 - x - 6 = 0 \\\\5 x^2 - 6 x + 5x- 6 = 0 \\\\5 x (x + 1)-6(x+1)=0\\\\x = -1 and (6)/(5)`

4.

`log(x-1)+log 5x = 2\\\\5 x (x-1) =2 \\\\5x^2 - 5x -2 = 0 \\\\x = (5\pm√(25+40))/(10)\\\\x = (5\pm 8)/(10)\\\\x = 1.3, - 0.3`