SOLUTION: 6 log p = 2,5 Then a value of p

Question 997751: 6 log p = 2,5
Then a value of p
Found 2 solutions by Alan3354, Theo:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
6 log p = 2,5
------
6log(p) = 2.5
log(p) = 2.5/6

p = ~2.61
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
6log(p) = 2.5
hopefully your comma represents a decimal point.
otherwise, i have no idea what you are asking.
i believe you can solve this a couple of ways.
i'll do both just to see if the same answer comes out.
first way:
divide both sides by 6 to get log(p) = 2.5/6
this is true if and only if 10^(2.5/6) = p
solve for p to get p = 2.610157216
confirm by replace p in the original equation with your answer.
6log(2.610157216) = 2.5 becomes 2.5 = 2.5, confirming the solution is correct.
second way:
6log(p) = 2.5 becomes log(p^6) = 2.5
this is true if and only if 10^2.5 = p^6
solve for p^6 to get p^6 = 316.227766
take the sixth root of each side of the equation to get p = 2.610157216.
same answer so both methods are good.

how do you take the 6th root of each side of the equation?
p^6 = 316.227766
(p^6)^(1/6) = 316.227766^(1/6)
(p^6)^(1/6) is the same as p^(6*1/6) which is the same as p^(6/6) which is the same as p^1 which is the same as p.
316.22776^(1/6) = 2.610157216
you are left with p = 2.610157216

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