From log (x2) + log (x4)/(log 70x) = 3, write 2log x +4 log x/(log 70+log x) = 3.
Multiply through 2log x +4log x/(log 70+log x) = 3 by (log 70+log x) to obtain
2log x(log 70+log x) + 4log x = 3(log 70+log x).
Then (2log 70)log x + 2(log x)2 + 4log x = 3log 70 + 3log x.
Further clarification gives (2log 70)log x + 2(log x)2 + log x = 3log 70,
which is rewritten as 2(log x)2 + (2log 70+1)log x − 3log 70 = 0 to follow
the form of a quadratic equation.
Then log x = {-(2log 70+1) ± √[(2log 70+1)2 − 4(2)(-3log 70)]}/2(2) which
will yield log x = 0.8627687106 or log x = -3.207866751.
Taking Common (Base 10) anti-logarithms, x = 7.290691312 or x = 0.0006196311594.
