> 
> Using the substitution $u=3^x$, or otherwise, solve, correct to 3 significant figures, the equation 
>  $3^x=2+3^{-x}$
> 
> 
> 

My attempt:

$u=2+u^{-1}$

$u-u^{-1}=2$

$ {{u^2-1}\over {u}}=2$

$\log ({{u^2-1}\over {u}})=\log (2)$

$\log ({u^2-1}) - \log ({u}) =\log (2)$

$\log ({(u-1)(u+1)}) -\log (u) = \log (2)$

$\log {(u-1)} + \log {(u+1)} -\log (u)= \log (2)$

Then what can I do please ?