[tex]e ^{2x} = ln5[/tex]
Solve for the real domain
[tex]e ^{2x} = ln(5)[/tex]
if [tex]f(x) =g(x),[/tex] then [tex]ln(f(x))= ln(g(x))[/tex]
[tex]ln(e ^{2x} ) = ln(ln(5))[/tex]
Solve : [tex]ln(e ^{2x} ) = ln(ln(5))[/tex]
use the logarithmic definition :
[tex]ln(e^{f(x)} ) = f(x)[/tex]
[tex]ln(e^{2x} ) = 2x[/tex]
[tex]2x=ln(ln(5))[/tex]
Divide both sides by 2 :
[tex] \frac{2x}{2} = \frac{ln(ln(5))}{2} [/tex]
[tex]x= \frac{ln(ln(5))}{2} [/tex]
hope this helps!
