505 MrG Solving Equations Using Inverse Functions!

2540 days ago by MATH4R2013

#1) 2*log(x)/log(5)==log(9)/log(5) equ=2*log(x)/log(5)==log(9)/log(5) show(equ) show(solve(equ,x)) show(solve(equ,x)[0]) show(solve(equ,x)[0].rhs()) show(solve(equ,x)[0].rhs().simplify_radical()) plot([2*log(x),log(9)],2,4,aspect_ratio=1) 
       





#2) log(x+3)/log(4)+log(2-x)/log(4)==1 plot([log(x+3)/log(4)+log(2-x)/log(4),1],-2.5,1.5,aspect_ratio=1) 
       
#3) 4^x-2^x-12==0 equ=4^x-2^x-12==0 show(equ) equ=(equ.simplify_radical()) show(equ) equ=factor(equ) show(equ) show(solve(equ,x)) show(solve(equ,x)[1].rhs().simplify_radical()) plot([4^x-2^x-12],0,3) 
       





#4) 8*3^x==5 equ=8*3^x==5 show(equ) equ=equ/8 show(equ) show(solve(equ,x)[0].rhs()) show(solve(equ,x)[0].rhs().n()) plot([8*3^x,5],-1,0) 
       




#5) 5^(x-2)==3^(3*x+2) plot([5^(x-2),3^(3*x+2)],-4,-3) 
       
#6) log(x)/log(3)+log(x)/log(4)==4 show(solve(log(x)/log(3)+log(x)/log(4)==4,x)[0].rhs()) show(solve(log(x)/log(3)+log(x)/log(4)==4,x)[0].rhs().n()) plot([log(x)/log(3)+log(x)/log(4),4],x,11,12) 
       


#7) x+e^x==2 plot([x+e^x,2])