Question 1038580
{{{log(x+1,(x^2 +x + 6 )^2) = 4}}}

==> {{{(x+1)^4 = (x^2 +x + 6 )^2}}}, or {{{2x^3-7x^2-8x-35 = 0}}}.

The roots of this polynomial are 5, {{{-3/4+(1/4)*sqrt(47)*i}}}, and {{{-3/4-(1/4)*sqrt(47)*i}}}.  (Go to http://www.mathportal.org/calculators/solving-equations/polynomial-equation-solver.php for a quick solution!)

Hence, x = 5.