2/3 e^4x+1/3=4 SOLVE?

Question

im confused can somone help me nicely.

Answer 1

2/3 e^4x + 1/3 = 4 (Separated constants terms of variable
term) => substracted by -1/3 both sides

2/3e^4x + 1/3 -1/3 = (4 -1/3

2/3e^4x + 0 = 11/3

2/3e^4x = 11/3 (Multiplied by 3/2 both sides)

(3/2) (2/3)e^4x = (3/2) 11/3

(1)e^4x = 33/6 (Simplified 33/6)

e^4x = 11/2 (Used '' ln '' both sides)

ln e^4x = ln(11/2) ( Applied this logarithm rule:
ln e^x = xln(e) )

4xln(e) = ln(5.5) ( n.b.: ln(e) = 1)

4x = 1.704748 (Multiplied by 1/4 both side)

(1/4) 4x = (1/4) 1.704748

x = 0.426187


Verification:

2/3 e^4(0.426187) + 1/3 = 4

(0.666666) e^1.704748 + 0.333333 = 4

(0.666666)(5.499999) + 0.333333 = 4

~ 3,999995 ~ 4

Answer 2

2/3 e^4x = 11/3
e^4x = 11/2
4x = ln(11/2)
x = (1/4)ln(11/2) = .426

Answer 3

x = 1/4ln(11/2) [about 0.4262]

Solution

2/3e^4x + 1/3 = 4

xbs 3

2e^4x + 1 = 12

Collect like terms and /bs 2

e^4x = 11/2

Take logs

4x = ln(11/2)

x = 1/4ln(11/2)

Answer 4

2.e^(4x) + 1 = 12
e^(4x) = 5.5
4x = ln 5.5
x = 1.705 / 4
x = 0.426 (to 3 dec. places)