1) х+2=9
х=7
2) 7^x=t; t^2-8t+7=0; t=1 и =7; 7^x=1 x=0; 7^x=7 x=1
3) log4(x-3)(x+1)=log421
x^2-2x-24=0
x=6 и x=-4 Но ОДЗ x-3>0 и х+1>0; x>3 и х>-1; x>3. Значит, х=6
4) sinx=t
10t^2-17t+16=0
t=34/20>1 и t=1/2. sinx=1/2; x=π/6 +2πn
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Answers & Comments
1) х+2=9
х=7
2) 7^x=t; t^2-8t+7=0; t=1 и =7; 7^x=1 x=0; 7^x=7 x=1
3) log4(x-3)(x+1)=log421
x^2-2x-24=0
x=6 и x=-4 Но ОДЗ x-3>0 и х+1>0; x>3 и х>-1; x>3. Значит, х=6
4) sinx=t
10t^2-17t+16=0
t=34/20>1 и t=1/2. sinx=1/2; x=π/6 +2πn