Пожалуйста помогите срочно как сможете 1) 2^x+2 - 2^x+1 + 2^x-1 - 2^x-2<=9<br>2) 3^2x-1 + 3^2x-2 - 3^2x-4<= 315<br>3) 2^x - 2^x-4>15 1) 25^x < 6*5^x - 5 2) 3^2x - 3*2^x + 2>0 3) 4^x + 2^x+3 > 20 4) 2^2x - 3*2^x + 2> 0
2) 3^2х-1 + 3^2х-2 -3^2х-4<=315; 3^2х/3 - 3^2х/3^2 - 3^2х/3^4<=315; 3^2х*(27+9-1)/81<=315; 3^2х<=315*81/35; 3^2х<=729; 3^2х<=3^6; 2х<=6; х<=3
3)2^х - 2^х-4 > 15; 2^х - 2^х/2^4 > 15; 2^х*(16-1)/16 > 15; 2^х > 15*16/15; 2^х > 16; 2^х > 2^4; х > 4
1)2^х+2 - 2^х+1 + 2^х-1 - 2^х-2<=9 <br>2^х*2^2 - 2^х*2 + 2^х/2 - 2^х/2^2<=9 <br>2^х(4-2+1/2-1/4)<=9 <br>2^х * 2 1/4<=9 <br>2^х<=4 <br>2^х<=2^2 <br>х<=2
1) x≤2 2) 2x≤6 x≤3 3) 15" alt=" 2^{x}- 2^{x-4} >15" align="absmiddle" class="latex-formula"> 15 " alt=" 2^{x}- \frac{ 2^{x} }{16}>15 " align="absmiddle" class="latex-formula"> 15 " alt=" 2^{x}(1- \frac{1}{16})>15 " align="absmiddle" class="latex-formula"> 16 " alt=" 2^{x}>16 " align="absmiddle" class="latex-formula"> x>4 1) 0 " alt=" 5^{x}=t; t>0 " align="absmiddle" class="latex-formula"> 0}} \right. " alt=" \left \{ {{ t^{2}-6t+5<0} \atop {t>0}} \right. " align="absmiddle" class="latex-formula"> t² - 6t + 5 < 0 t₁ = 1 t₂ = 5 t∈ (1;5), т.е. 11} \atop {t<5}} \right. " alt=" \left \{ {{t>1} \atop {t<5}} \right. " align="absmiddle" class="latex-formula"> 1 } \atop { 5^{x}<5 }} \right. " alt=" \left \{ {{ 5^{x}>1 } \atop { 5^{x}<5 }} \right. " align="absmiddle" class="latex-formula"> 0} \atop {x<1}} \right. " alt=" \left \{ {{x>0} \atop {x<1}} \right. " align="absmiddle" class="latex-formula"> x∈ (0;1) 3) 20 " alt=" 4^{x}+ 2^{x+3}>20 " align="absmiddle" class="latex-formula"> 0 " alt=" 2^{2x}+ 2^{x}*8 -20>0 " align="absmiddle" class="latex-formula"> 0 " alt=" 2^{x}=t; t>0 " align="absmiddle" class="latex-formula"> 0 } \atop {t>0}} \right. " alt=" \left \{ {{ t^{2}+8t-20>0 } \atop {t>0}} \right. " align="absmiddle" class="latex-formula"> t² + 8t - 20 >0 D₁ = 16 + 20 = 36 t₁ = -4+6 = 2 t₂ = -4-6 = -10 t∈ (-беск.;-10)U(2;+беск.), но так как t>0, то t∈ (2; + беск.) или t>2 2" alt=" 2^{x} >2" align="absmiddle" class="latex-formula"> x>1 4) 0 " alt=" 2^{2x}-3* 2^{x}+2>0 " align="absmiddle" class="latex-formula"> 0 " alt=" 2^{x}=t; t>0 " align="absmiddle" class="latex-formula"> 0 } \atop {t>0}} \right. " alt=" \left \{ {{ t^{2}-3t+2>0 } \atop {t>0}} \right. " align="absmiddle" class="latex-formula"> t² - 3t + 2 >0 t₁ = 1 t₂ = 2 t ∈ (-беск.; 1)U(2;+беск.) так как t>0, то t ∈ (0;1) U (2; + беск.) или: 2 }} \right. " alt=" \left \{ {{ 2^{x}<1 } \atop { 2^{x}>2 }} \right. " align="absmiddle" class="latex-formula"> 1}} \right. " alt=" \left \{ {{x<0} \atop {x>1}} \right. " align="absmiddle" class="latex-formula"> x ∈ (-беск.;0) U (1;+беск.)