Question

log^2(100x) +log^2(10x)=14+log(1/x)

Answer 1

(log 100 + log x) ^2+ (log 10 + log x)^2 =14 - logx
(2+ log x)^2 + (1 + log x) ^2 + log x - 14 = 0
(4 + log^2 x + 4 log x) + (1 + log^2 x + 2 log x) + log x - 14 = 0
simplifying,
2 log^2 x + 7 log x - 9 = 0
splitting the middle term,
2 log^2 x - 2 log x + 9 log x - 9 = 0
2 log x ( log x - 1) + 9 ( log x - 1) =0
2 log x + 9 = 0
log x = -9/2
x^-9/2 =1
implies x =1