1.

(log3 x)^2 - 3log3 x + 2 > 0

Замена: log3 x = t

t^2 - 3t + 2 > 0

t^2 - 3t + 2 = 0

По теореме Виета:

t1 = 1

t2 = 2

t є (-оо; 1) U (2; +oo)

log3 x є (-оо; 1) U (2; +oo)

x є (0; 3) U (9; +oo)

2.

1/(3 - lg x) + 1/(1 + lg x) > 1

Замена: lg x = t

1/(3 - t) + 1/(1 + t) > 1

(1 + t + 3 - t - (3 - t)(1 + t)) / (3 - t)(1 + t) > 0

(4 - (3 + 3t - t - t^2)) / (3 - t)(1 + t) > 0

(t^2 - 2t + 1) / (3 - t)(1 + t) > 0

(t - 1)^2 / (3 - t)(1 + t) > 0

-1 1 3

—-o—-o—-o—-> t

(-) (+) (+) (-)

t є (-1; 1) U (1; 3)

lg x є (-1; 1) U (1; 3)

x є (0,1; 10) U (10; 1000)