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Question

Решить неравенства:

1)2^{x+1}<32</p>

2)0.2^{3x-4}>1

3)0.3^{2x-1}>0.3

4)0.5^{2x-1}<1</p>

5)3^{6-x}>1

Answer 1

1) 2^{x+1}<2^5, x+1<5, x<4</p>

2) 0.2^{3x-4}>0.2^0, 3x-4>0, x>4/3

3) 0.3^{2x-1}>0.3^1, 2x-1>1, 2x>2, x>1

4) 0.5^{2x-1}<0.5^0, 2x-1<0, x<1/2</span>

5)3^{6-x}>3^0, 6-x>0, x<6</span>

Answer 2

1) 2^(x+1) < 2^5 => x+1 < 5 =>  x<4</p>

2) 0.2 ^ (3x -4) > 0.2^0 => 3x -4 >0 => 3x >4 => x > 4/3

3) 0.3^(2x -1) > 0.3 ^1  => 2x-1>1 => 2x>2 => x>1

4)0.5^(2x - 1) < 0.5^0 => 2x -1 <0 => 2x <1 => x < 0.5

5) 3 ^(6 - x) > 3^0 => 6 - x >0 => x<6</p>