Which is the only solution to the equation log₃(x² + 6x) = log₃(2x + 12)?
x = -6, x = -2, x = 0, x = 2, x = 6

Solution:

It is given that expression is

log₃(x² + 6x) = log₃(2x + 12)

Let us make use of the logarithmic rule

log_b x = log_b y

So x = y

x² + 6x = 2x + 12

By subtracting 2x on both sides

x² + 6x - 2x = 2x + 12 - 2x

x² + 4x = 12

It can be written as

x² + 4x - 12 = 0

Splitting the middle term

x² + 6x - 2x - 12 = 0

Taking out the common terms

x(x + 6) - 2(x + 6) = 0

(x + 6)(x - 2) = 0

So we get

x + 6 = 0 and x - 2 = 0

x = - 6 and x = 2

As x = -6 does not satisfy the equation, x = 2 is the only solution.

Therefore, the only solution is x = 2.

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

Summary:

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