Question

what is the minimum value of k for which
4^k+5^k<6^k
is there an analytic way?

Answer 1

there is no value of k for which the equation holds true

Answer 2

yes there is .. k =3

Answer 3

lemme check

Answer 4

yepp. the value will lie between 2 and 3. Sorry, cant think of any analytic way right now

Answer 5

In[70]:= FindRoot[ 4^x + 5^x == 6^x, {x, 2}]

Out[70]= {x -> 2.48794}