3^(x+1)=4^(x-1) Solve for X

3^(x+1)=4^(x-1)      take the log of both sides

log 3 ^(x + 1)  = log 4^(x - 1)   and we can write

(x + 1) log 3   = (x - 1)log 4     simplify

x log 3 + log 3 =  xlog 4 - log 4        rearrange

x log 3 - x log 4 =   - log 3 - log 4         multiply through by  -1

xlog 4 - x log 3 = log 4 +  log 3      factor out x

x [ log 4 - log 3 ]   = log 4 + log 3          divide both sides by [ log 4 - log 3]

x =  [ log 4 + log 3 ] / [ log 4 - log 3]  ≈  8.6377