Answer:
If [tex]k > 0[/tex], then [tex]x[/tex] must be greater than 0.
Step-by-step explanation:
If [tex]k > 0[/tex], then we state that [tex]e^{5\cdot x} > 0[/tex] and [tex]e^{5\cdot x}[/tex] is a trascendental function with a lower bound so that [tex]e^{5\cdot x}> 1[/tex]. Then, the minimum value of [tex]k[/tex] is 1 and we proceed to solve the latter equation to find the value of [tex]x[/tex]:
[tex]e^{5\cdot x}> 1[/tex]
[tex]\ln e^{5\cdot x} > \ln 1[/tex]
[tex]5\cdot x > 0[/tex]
[tex]x > 0[/tex]
Therefore, [tex]x[/tex] must be greater than 0.
