SOLUTION: 3^(3x+1)=6^(x+2)

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Question 1031793: 3^(3x+1)=6^(x+2)
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

3%5E%283x%2B1%29%22%22=%22%226%5E%28x%2B2%29

log%28%283%5E%28%283x%2B1%29%29%29%29%22%22=%22%22log%28%286%5E%28%28x%2B2%29%29%29%29

%283x%2B1%29log%28%283%29%29%22%22=%22%22%28x%2B2%29log%28%286%29%29

Let A = log(3) and let B = log(6)

%283x%2B1%29A%22%22=%22%22%28x%2B2%29B

A%283x%2B1%29%22%22=%22%22B%28x%2B2%29

3Ax%2BA%22%22=%22%22Bx%2B2B

3Ax-Bx%22%22=%22%222B-A

x%283A-B%29%22%22=%22%222B-A

x%283A-B%29%2F%283A-B%29%22%22=%22%22%282B-A%29%2F%283A-B%29

x%28cross%283A-B%29%29%2F%28cross%283A-B%29%29%22%22=%22%22%282B-A%29%2F%283A-B%29

x%22%22=%22%22%282B-A%29%2F%283A-B%29

Substitute log(3) for A and log(6) for B

x%22%22=%22%22%282log%28%286%29%29-log%28%283%29%29%29%2F%283log%28%283%29%29-log%28%286%29%29%29

Get calculator:
 
x%22%22=%22%22%282%280.7781512504%29-%280.4771212547%29%29%2F%283%280.4771212547%29-%280.7781512504%29%29

x%22%22=%22%221.652113552

Edwin