Question

Which is the only solution to the equation log3(x2 + 6x) = log3(2x + 12)?

x = –6

x = –2

x = 0

x = 2

x = 6

Answer 1

the answer is option 4: x=2

Answer 2

Option 4th is correct

x = 2

Explanation:

Using logarithmic rule:

`\log_b x = \log_b y`

then; x = y

Given the equation:

`\log_3 (x^2+6x) = \log_3 (2x+12)`

Apply the rule:

`x^2+6x = 2x+12`

Subtract 2x from both sides we have;

`x^2+4x =12`

Subtract 12 from both sides we have;

`x^2+4x-12=0`

⇒
`x^2+6x-2x-12 = 0`

⇒
`x(x+6)-2(x+6)= 0`

⇒
`(x+6)(x-2)= 0`

by zero product property we have:

x+6 =0 and x-2 = 0

⇒x= -6 and x = 2

Since, at x = -6 it does not satisfy the given equation.

Therefore, the only solution to the given equation is, x = 2