SOLUTION: Given that log3 p = q , find q^(q+2) in terms of p .

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Question 898371: Given that log3 p = q , find q^(q+2) in terms of p .
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
you are given that log3(p) = q.

q^(q+2) should therefore be equal to log3(p)^(log3(p) + 2)

let's assume that q is equal to 2.

log3(p) = q if and only if 3^q = p

since q = 2, then p must be equal to 9.

you get:

log3(9) = 2

this is true if and only if 3^2 = 9 which it is, so the statement is true.

q^(q+2) is equivalent to log3(p) ^ (log3(p) + 2)

since p is equal to 9, then q^(q+2) must be equal to log3(9) ^ ( log3(9) + 2)

since log3(9) = 2, then we get log3(9)^(log3(9) + 2) = 2^(2+2) which is equal to 2^4.

we also get q^(q+2) = 2^(2+2) = 2^4 as well.

i think your answer is that:

q^(q+2) in terms of p is equal to log3(p)^(log3(p) + 2)