Exercices - Logarithmes et exponentielles

Résoudre

equation[1]=(Log[x]^2-Log[x]-2==0);
equation[2]=(Log[x]^4-3Log[x]^2+2==0);
equation[3]=(Log[2x-3]+Log[x-4]==2Log[5]);
equation[4]=(Log[2x-3]-Log[x-4]==2Log[5]);
equation[5]=(2 Log[x-3]+Log[x-1]==Log[2x-2]);
equation[6]=(20Log[x]^2-16Log[x]+3==0);
equation[7]=(HoldForm[4^x-2^(x+3)-128==0]);
equation[8]=(3^x+3^(3-x)==12);
equation[9]=(HoldForm[Log[x,Sqrt[2]]]==3);
equation[10]=(HoldForm[Log[6,x]]+HoldForm[Log[x,6]]==13/6);
equation[11]=(2 HoldForm[Log[4,x+1]]+HoldForm[Log[4,x+3]]==1/2+HoldForm[Log[4,6x+2]]);
equation[12]=(HoldForm[Log[2,x-1]]==HoldForm[Log[4,3]]);
equation[13]=(HoldForm[Log[7,3x-1]]==-1/2);
equation[14]=(HoldForm[Log[3,Log[4,x]]]==-1);
equation[15]=(HoldForm[Log[2,Log[x,81]]]==2);
equation[16]=(HoldForm[E^x-4E^(-x)-3]==0);
equation[17]=(HoldForm[Log[x-1,5x]]==2);
equation[18]=(10^(2x)-10^x==5);
equation[19]=(81^x+81^(1-x)==30);
equation[20]=(HoldForm[Log[10,x+1]]-2==HoldForm[Log[5,0.2]]);
(* inéquations *)
equation[21]=(HoldForm[Log[1/3,(1-x^2)/x]]<HoldForm[Log[3,x]]);
equation[22]=(4-Log[x]^2≤0);
equation[23]=(Log[x]-Log[2]≤Log[1-3x]);
equation[24]=((Log[x]+1)/(1-Log[x])≤0);
equation[25]=(2Log[x]^2-Log[x]-1≥0);
equation[26]=(Exp[x]+2Exp[-x]-3>0);
equation[27]=(Exp[2x+1]+1/Exp[1]>0);
equation[28]=(HoldForm[(1/E)^x]-Exp[1]^(3x-1)≤0);
equation[29]=(Log[(x-1)/(x+1)]+Log[x]<0);
equation[30]=(Log[Exp[x]+2]≥Log[4-Exp[x]]);

equation[31]=(HoldForm[Log[1/5,3x-1]]≤5);
equation[32]=(HoldForm[Log[7,(1-x)/(1+x)]]≥0);

equation[33]=(HoldForm[Log[1/5,5]]==x);
equation[34]=(HoldForm[Log[x-4,4x]]==2);
equation[35]=(Sqrt[5^x]+2/Sqrt[5^x]==3);

Do[solution[i]=Equalogexp[equation[i],x],{i,35}];
Do[Print[i,") ",equation[i]],{i,35}];

Solutions

Do[Print[i,") S = ",solution[i]],{i,35}];