Question

What is the solution to the equation below? Round your answer to two

decimal places.
5e2x + 16 = 56
OA. x=2.08
OB. x= 1.04
OC. X= 4.16
OD. x= 1.78

Answer 1

B

Explanation:

using the rules of logarithms

• ln e = 1 ( ln is the natural logarithm or
`log_(e)` )

• log
`a^(x)` = x loga

given the equation

5
`e^(2x)` + 16 = 56 (subtract 16 from both sides )

5
`e^(2x)` = 40 ( divide both sides by 5 )

`e^(2x)` = 8 ( take ln of both sides )

ln
`e^(2x)` = ln8, that is

2x lne = ln8 ( lne = 1 )

2x = ln8 ( divide both sides by 2 )

x =
`(ln8)/(2)` ≈ 1.04 ( to 2 decimal places )