SOLUTION: How can you solve 6^x+2=3^x+1 with out the calculator? I think you really can't because I tried it with the calculator and x comes out to be -3.584... so then the exponent would be

Question 195908: How can you solve 6^x+2=3^x+1 with out the calculator? I think you really can't because I tried it with the calculator and x comes out to be -3.584... so then the exponent would be a negative number...so I can't use logs.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
6^(x+2) = 3^(x+1)
(x+2)log6 = (x+1)log3
---
[log(6)-log(3)]x = [log(3) - 2log(6)]
---
x = [log(3) - 2log(6)] / [log(6)-log(3)]
x = log(3/6^2) / log(2)
---
x = log(1/12)/log(2)
x = log(base 2) (1/12)
=================================
Cheers,
Stan H.
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