Answer
$x \approx 2.262$
Work Step by Step
$2^{x+1}=6^{x-1}$
$\ln 2^{x+1}=\ln 6^{x-1}$
$(x+1) \ln 2 = (x-1) \ln 6$
$(\ln 2)x + \ln2 = (\ln 6) x- \ln 6$
$\ln 2 + \ln 6 = (\ln 6 - \ln 2)x$
$x = \frac{\ln 2 + \ln 6}{\ln 3} \approx 2.262$
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