If log_3 (x) + log_3 (x + 6) = 3, what is the value of x?
Show the answer and explanation
Correct answer
A. 3
Principle or equation
Use logarithm product rule: log_a M + log_a N = log_a (MN). Convert to exponential form.
Why this answer is correct
log_3 [x(x+6)] = 3 => x(x+6) = 3^3 = 27 => x^2 + 6x - 27 = 0 => (x+9)(x-3)=0 => x = -9 or 3. Since log argument must be positive, x = 3.
Example
Solve log_2 (x) + log_2 (x+2) = 3: x(x+2)=8 => x=2.
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