Determine the decimal values, if there is anyI don't have a clue wheather there is a decimal value of x if the expression 5e^x-3e^x=2?

Asked on by abigaile

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to factor out ` e^x` such that:

`e^x(5 - 3) = 2 => 2e^x = 2 => 2e^x - 2 = 0`

You need to factor out 2 such that:

`2(e^x - 1) = 0 => {(2!= 0),(e^x - 1 = 0):} => e^x = 1`

Replacing `e^0` for 1 yields:

`e^x = e^0`

Equating the exponents yields:

`x = 0`

Hence, evaluating the solution to exponential equation yields `x = 0.`

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

5e^x - 3e^x = 2

We'll combine like terms from the left side:

2e^x = 2

We'll divide by 2:

e^x = 1

Now, we'll have to determine x, that is the exponent of e. For this reason, we'll take natural logarithms both sides:

ln e^x = ln 1

We'll apply the power rule of logarithms:

x* ln e = ln 1

By definition, ln e = 1 and ln 1 = 0 and we'll substitute it into equation:

x = 0

There is no decimal value for x in this case