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

InterviewSolution

1.	`log^2(100x)+log^2(10x)=14+log(1/x)`
Answer» `log^2(100x)+log^2(10x) = 14+log(1/x)` `=>log(100x)^2+log(10x)^2 = 14-logx` `=>(log100+logx)^2+(log10+logx)^2 = 14-logx` `=>(2+logx)^2+(1+logx)^2 = 14-logx` Let, `logx = t`, then our equation becomes, `(2+t)^2+(1+t)^2 = 14 - t` `=>4+t^2+4t+1+t^2+2t+t - 14 = 0` `=>2t^2+7t-9 = 0` `=>(2t+9)(t-1) = 0` `=> t = -9/2 and t = 1` `=>logx = -9/2 and logx = 1` `:. x = 10^(-9/2) and x = 10^1 =10`

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