Need to solve only 515355 and 57 In Exercises 5158 use the O

In Exercises 51-58, use the One-to-One Property to solve the equation for x. 51. 3+1- 27 53. 55. e3+2 e3 57. e2x 52, 2-3 = 16 54. 5-2 =12 56. e2x-1e 71 2x-1 =

Solution

51)3^x+1=27

3^x+1=3³

x+1=3

x=2

53)(1/2)^x=32

(2^-1)^x=2⁵

2^-x=2⁵

-x=5

x=-5

55)e^3x+2=e³

3x+2=3

3x=1

x=1/3

57)e^{x^2 -3}=e^2x

x²-3=2x

x²-2x-3=0

x²-3x+x-3=0

x(x-3)+1(x-3)=0

(x+1)(x-3)=0

x+1=0 ,x-3=0

x=-1,x=3

x=-1,3