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Question Number 159639 by bobhans last updated on 19/Nov/21

((x−1)/(log _3 (9−3^x )−3)) ≤ 1

x−1log3(9−3x)−3⩽1

Answered by tounghoungko last updated on 19/Nov/21

((x−1)/(log _3 (9−3^x )−log _3 (27))) ≤ 1 ; 9−3^x >0 ; x<2 ((x−1)/(log _3 (((9−3^x )/(27))))) ≤ 1 (x−1)log _((((9−3^x )/(27)))) (3) ≤ 1 log _((((9−3^x )/(27)))) (3^(x−1) ) ≤ 1 as x<2 , 0 < ((9−3^x )/(27)) < 1 3^(x−1 ) ≥ ((9−3^x )/(27)) 9.3^x ≥ 9−3^x ; 10.3^x ≥ 9 x ≥ log _3 ((9/(10))) then x∈ [ log _3 ((9/(10))) , 2 )

x−1log3(9−3x)−log3(27)⩽1;9−3x>0;x<2x−1log3(9−3x27)⩽1(x−1)log(9−3x27)(3)⩽1log(9−3x27)(3x−1)⩽1asx<2,0<9−3x27<13x−1⩾9−3x279.3x⩾9−3x;10.3x⩾9x⩾log3(910)thenx∈[log3(910),2)

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