l4times5e2times240 52times54times125Solution1 e4x 5e2x 24 0

l4times+5e^2times-24=0 5^2times.5^4times=125

1) e^4x + 5e^2x -24 =0

Let e^2x =y

y^2 +5y -24 =0

factosrie: y^2 +8y-3y -24 =0

(y+8) -3(y+8) =0

(y-3)(y+8) =0

y = 3---->e&2x = 3

taking log on both sides:

2x = ln(3)

x= ln(3)/2

y = -8

e^2x = -8 This is not a solution asexpoenetila cannot giev -ve value

So, solution : x= ln(3)/2

2) 5^2x*5^4x = 125

5^(2x+4x) = 125

5^(6x) = 5^3

If base are same we can equate the exponents:

6x = 3

x= 1/2