SOLUTION: Solve3.7P=2.6^logP

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Question 268916: Solve3.7P=2.6^logP
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Here is the original problem
(i) 3.7P=2.6%5ElogP
step 1 - take a log of both sides to get
(ii) log%283.7P%29=log%282.6%5ElogP%29
step 2 - using power rule on the right side we get
(iv) log%283.7P%29=log%28P%29%2Alog%282.6%29
step 3 - using rules of logs on the left we get
(v) log%283.7%29+%2B+log%28P%29=log%28P%29%2Alog%282.6%29
step 4 - subtracting log(P) we get
(vi) log%283.7%29+=+log%28P%29%2Alog%282.6%29+-+log%28P%29
step 5 - factoring, we get
(vii) log%283.7%29+=+log%28P%29%2A%28log%282.6%29+-+1%29
step 6 - divide to get
(viii) log%283.7%29%2F%28log%282.6%29-1%29+=+log%28P%29
step 7 - raise all to 10^ to get
.
.
.
(xi) 10%5E%28log%283.7%29%2F%28log%282.6%29-1%29%29+=+P
So, we get
P ~ .106846