Question

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

Answer 1

Answer:

Option 4th is correct

x = 2

Step-by-step 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

Answer 2

the answer is option 4: x=2