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

x = –6

x = –2

x = 0

x = 2

x = 6

the answer is option 4: x=2

Option 4th is correct

x = 2

Step-by-step explanation:

Using logarithmic rule:

then; x = y

Given the equation:

Apply the rule:

Subtract 2x from both sides we have;

Subtract 12 from both sides we have;

⇒

⇒

⇒

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

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