SOLUTION: Solve for x: 3^x+2 plus 3^x = 270 Please use steps God bless How to answer this quesiton with logs appearing in at least one of the steps? Thanks:)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Solve for x: 3^x+2 plus 3^x = 270 Please use steps God bless How to answer this quesiton with logs appearing in at least one of the steps? Thanks:)      Log On


   

Question 133441: Solve for x: 3^x+2 plus 3^x = 270
Please use steps
God bless
How to answer this quesiton with logs appearing in at least one of the steps?
Thanks:)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3%5E%28x%2B2%29%2B3%5Ex+=+270 Start with the given equation


3%5Ex%2A3%5E2%2B3%5Ex+=+270 Rewrite 3%5E%28x%2B2%29 as 3%5Ex%2A3%5E2


3%5Ex%2A%283%5E2%2B1%29+=+270 Factor out 3%5Ex


3%5Ex%2A%289%2B1%29+=+270 Evaluate 3%5E2 to get 9


3%5Ex%2A%2810%29+=+270 Add


3%5Ex+=+27 Divide both sides by 10



log%2810%2C%283%5Ex%29%29+=+log%2810%2C%2827%29%29 Take the log of both sides


x%2Alog%2810%2C%283%29%29+=+log%2810%2C%2827%29%29 Rewrite the left side using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


x+=+log%2810%2C%2827%29%29%2Flog%2810%2C%283%29%29 Divide both sides by log%2810%2C%283%29%29


x+=+log%283%2C%2827%29%29 Combine the logs


x+=+3 Evaluate log%283%2C%2827%29%29 to get 3



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Answer:

So the answer is x+=+3