Solve for x:

3^(x+1)=2^x

This is what I have so far...
(x+1)log3 = xlog2

...and now I'm stuck. Help plz? Thanks!

2 answers

that is it, so x+1=x (log2/log3)

x(1-log2/log3)=-1
solve for x
expand the left side ...
xlog3 + log3 = xlog2
xlog3 - xlog2 = -log3
x(log3-log2) = -log3
x = -log3/(log3 - log2)

I got x = appr. - 2.7095

check:
3^(-1.7095) = .15288
2^-2.7095 = .15288 , Ok!
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