Math Help - Logarithmic Equation

1. Logarithmic Equation

I have a problem, whose solution, apperantly, eludes me.
I have chosen to upload it as a .gif file. The second equation is what I get after the obvious substitution and simplification. This is not correct, the answer is suppsed to be t=3, hence x = 1000, and I fail to find my mistake, which is why I am asking for help.
Thank you.

2. $\sqrt{1 + \log{x}} + \sqrt{2\log{x} - 2} = 4$

let $t = \log{x}$

$\sqrt{1 + t} + \sqrt{2t - 2} = 4$

$(1+t) + 2\sqrt{(1+t)(2t-2)} + (2t-2) = 16$

$2\sqrt{(1+t)(2t-2)} = 17-3t$

$4(1+t)(2t-2) = (17-3t)^2$

$8t^2 - 8 = 9t^2 - 102t + 289$

$0 = t^2 - 102t + 297$

$0 = (t - 3)(t - 99)$

t = 3, t = 99

log(x) = 3, x = 1000

log(x) = 99 is an extraneous solution

3. Thank you. I have now understood my mistake. A silly one it was, as expected.