E^(2x) = ln 5 (solve with explanation)

Question

`e^(2x) = ln 5` (solve with explanation)

Answer 1

`e ^(2x) = ln5`

Solve for the real domain


`e ^(2x) = ln(5)`

if
`f(x) =g(x),` then
`ln(f(x))= ln(g(x))`


`ln(e ^(2x) ) = ln(ln(5))`

Solve :
`ln(e ^(2x) ) = ln(ln(5))`

use the logarithmic definition :


`ln(e^(f(x)) ) = f(x)`


`ln(e^(2x) ) = 2x`


`2x=ln(ln(5))`

Divide both sides by 2 :


`(2x)/(2) = (ln(ln(5)))/(2)`


`x= (ln(ln(5)))/(2)`

hope this helps!