SOLUTION: 2^(3x+1)= 3^(x-2) I get log base 2^3^(x-2)= 3x+1 and I am stuck after this. Any suggestions? Thanks so much

Question 466762: 2^(3x+1)= 3^(x-2)

I get log base 2^3^(x-2)= 3x+1 and I am stuck after this. Any suggestions?
Thanks so much
Found 2 solutions by Alan3354, ccs2011:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
2^(3x+1)= 3^(x-2)
(3x+1)*log(2) = (x-2)*log(3)
3x*log(2) + log(2) = x*log(3) - 2log(3)
x*log(8) - x*log(3) = -log(2) - log(9)
x*log(8/3) = -log(18)
x = -log(18)/log(8/3)
x =~ -2.9469

Answer by ccs2011(207) (Show Source): You can put this solution on YOUR website!
Good so far, took log of both sides
For simplicity sake, when I use log i am using log base 2.

From here you need to use the following log property:

This will get the variable x out of the exponent

Distribute right side

Get x's on left side, constants on right

Factor out the x on left, and factor out negative on right

Divide by (3 - log 3) on both sides

If you use your calculator this is approximately

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