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Math really teaches you to try the easy way first to be more efficient
Ha-ha-ha, crazy solution! This problem is for kids at schools. 1/2 - is an obvious solution. And unique because y=4^(-x) is decreasing function, y=x - increasing.
1/4^x = x:try 1, 1/4=1try higher 2, 1/16 = 2, wrong direction, try lower 1/2, 1/2 = 1/2thus x = 1/2trial and error, takes about 20 seconds
You don't know if it's the only solution (or if a solution exists)
4^-x=x; 4^(-x)^-1/x =x^-(-1)(1/x);=>4=(1/x)^1/x=4=2^2; =>1/x=2; x=1/2
1=x*e^(x*ln4) , ln4=x*ln4*e^(x*ln4) , 2*ln2=x*ln4*e^(x*ln4) , ln2*e^(ln2)=x*ln4*e^(x*ln4) , ln2=x*ln4 , ln2=x*2*ln2 , 2x=1 , x=1/2 , test , OK ,
Are you mad?
Math really teaches you to try the easy way first to be more efficient
Ha-ha-ha, crazy solution! This problem is for kids at schools. 1/2 - is an obvious solution. And unique because y=4^(-x) is decreasing function, y=x - increasing.
1/4^x = x:
try 1, 1/4=1
try higher 2, 1/16 = 2, wrong direction,
try lower 1/2, 1/2 = 1/2
thus x = 1/2
trial and error, takes about 20 seconds
You don't know if it's the only solution (or if a solution exists)
4^-x=x; 4^(-x)^-1/x =x^-(-1)(1/x);=>4=
(1/x)^1/x=4=2^2; =>1/x=2; x=1/2
1=x*e^(x*ln4) , ln4=x*ln4*e^(x*ln4) , 2*ln2=x*ln4*e^(x*ln4) , ln2*e^(ln2)=x*ln4*e^(x*ln4) , ln2=x*ln4 , ln2=x*2*ln2 , 2x=1 , x=1/2 , test , OK ,
Are you mad?