SOLUTION: solve for x {{{log(2,(3x+4))-log(2,(2-3x))=3}}} please show working thank you

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Question 153274: solve for x
log%282%2C%283x%2B4%29%29-log%282%2C%282-3x%29%29=3

please show working
thank you
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
log%282%2C%283x%2B4%29%29-log%282%2C%282-3x%29%29=3 

Use rule of logs:  log%28b%2CA%29-log%28b%2CC%29=log%28b%2CA%2FC%29

log%282%2C%28%283x%2B4%29%2F%282-3x%29%29%29=3

Use rule of logs: Log equation log%28b%2CA%29=C can be written
                  as exponential equation A=b%5EC   

%283x%2B4%29%2F%282-3x%29=2%5E3 

                    2%5E3=2%2A2%2A2=8

%283x%2B4%29%2F%282-3x%29=8

                  Multiply both sides by 2-3x

3x%2B4=8%282-3x%29

                  Distribute the 8   

3x%2B4=16-24x%29

                  Get x's alone on left side

27x=12

                  Divide both sides by 27 
x=12%2F27

                  Reduce the fraction  

x=4%2F9

Edwin