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Hope you can help to solve this problem. logbase3 P = Q. Express Q power Q+2 in terms of P.

Hope you can help to solve this problem. logbase3 P = Q. Express Q power Q+2 in terms of P. The question is from the activity book and the answer is 81P square

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Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
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“log_3(P) = Q. Express Q^(Q+2) in terms of P.
Answer: 81P^2”

Take log_3 of the “Answer”:

log_3(81P^2) = log_3(3^4) + log_3(P^2)
= 4 log_3(3) + 2 log_3(P)
= 4 + 2Q = 2(Q+2)

Find equivalent exponential form:

81P^2 = 3^(2(Q+2)) = 9^(Q+2)

So the only way 81P^2 = Q^(Q+2) is if Q = 9.

IS THE QUESTION POSED CORRECTLY?