Given:
[tex]4(2.5)^{2x}=4[/tex]Required:
We need to find the value of x.
Explanation:
Divide both sides of the given equation by 4.
[tex]\frac{4(2.5)^{2x}}{4}=\frac{4}{4}[/tex][tex](2.5)^{2x}=1[/tex]Take a natural log on both sides.
[tex]In(2.5)^{2x}=In(1)[/tex][tex]Use\text{ }In(a^b)=bIn(a).[/tex][tex]2xIn(2.5)=In(1)[/tex]Use In (1) =0 in the equation.
[tex]2xIn(2.5)=0[/tex][tex]x=0[/tex]Final answer:
The value of x is 0.