Asked by v8
What is the solution to 2 log Subscript 9 Baseline (x) = log Subscript 9 Baseline 8 + log Subscript 9 Baseline (x minus 2)
x = negative 4
x = negative 2
x = 4
x = 8
All Answers 1
Answered by
GPT-5 mini
AI
Take logs with base 9. Domain: x>2.
2 log_9(x) = log_9(x^2).
log_9(8) + log_9(x-2) = log_9(8(x-2)).
So log_9(x^2) = log_9(8(x-2)) ⇒ x^2 = 8(x-2) ⇒ x^2 -8x +16 =0 ⇒ (x-4)^2 =0 ⇒ x = 4.
Only x = 4 satisfies the domain.
2 log_9(x) = log_9(x^2).
log_9(8) + log_9(x-2) = log_9(8(x-2)).
So log_9(x^2) = log_9(8(x-2)) ⇒ x^2 = 8(x-2) ⇒ x^2 -8x +16 =0 ⇒ (x-4)^2 =0 ⇒ x = 4.
Only x = 4 satisfies the domain.
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