SOLUTION: solve for x: 2^(x-1) = 3^(2x+1) Answer is: Log2+log3/log2-2log3 = -1.191 Please help to arrive at answer. Thank you! Tiffany

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: solve for x: 2^(x-1) = 3^(2x+1) Answer is: Log2+log3/log2-2log3 = -1.191 Please help to arrive at answer. Thank you! Tiffany      Log On


   

Question 972068: solve for x: 2^(x-1) = 3^(2x+1) Answer is: Log2+log3/log2-2log3 = -1.191
Please help to arrive at answer.
Thank you!
Tiffany
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2%5E%28x-1%29+=+3%5E%282x%2B1%29


log%28%282%5E%28x-1%29%29%29+=+log%28%283%5E%282x%2B1%29%29%29 Apply logs to both sides (to isolate exponents)


%28x-1%29%2Alog%28%282%29%29+=+%282x%2B1%29%2Alog%28%283%29%29 Use rule 3 (from this link)


x%2Alog%28%282%29%29-log%28%282%29%29+=+2x%2Alog%28%283%29%29%2Blog%28%283%29%29 Distribute


x%2Alog%28%282%29%29+=+2x%2Alog%28%283%29%29%2Blog%28%283%29%29%2Blog%28%282%29%29 Add log%28%282%29%29 to both sides.


x%2Alog%28%282%29%29-2x%2Alog%28%283%29%29+=+log%28%283%29%29%2Blog%28%282%29%29 Subtract 2x%2Alog%28%283%29%29 from both sides.


x%28log%28%282%29%29-2%2Alog%28%283%29%29%29+=+log%28%283%29%29%2Blog%28%282%29%29 Factor out the GCF x


x+=+%28log%28%283%29%29%2Blog%28%282%29%29%29%2F%28log%28%282%29%29-2%2Alog%28%283%29%29%29 Divide both sides by log%28%282%29%29-2%2Alog%28%283%29%29 to isolate x.


x+=+%28log%28%282%29%29%2Blog%28%283%29%29%29%2F%28log%28%282%29%29-2%2Alog%28%283%29%29%29 Rearrange terms. This is the exact answer in terms of logs.


x+=+-1.19126813092756 Use a calculator to get the approximate answer


x+=+-1.191 Round to 3 decimal places (again this is approximate)