Question

FIND THE SOLUTION: e^(3x-2)=e^(x)

Answer 1

x = 1

Explanation:

since y = e^x is a function that has unique y-values for any x-value (there are no 2 x-values that have the same y-value), we know that

e^x1 = e^x2 means that

x1 = x2

so, in our case

e^(3x - 2) = e^x

means

3x - 2 = x

we can also apply the logarithm on both sides to prove that

ln(e^(3x - 2)) = ln(e^x)

3x - 2 = x

so, now, we subtract x from both sides

2x - 2 = 0

add 2 to both sides

2x = 2

and divide both sides by 2

x = 1

Answer 2

Hello !

Answer:

`\Large \boxed{\sf x=1}`

Explanation:

We want to find the value of x that satisfies the following equation :

`\sf e^(3x-2)=e^(x)`

Let's remember :

• 
  `\sf ln(e^a)=a`

Let's apply
`\sf ln` to both sides of the equality :

`\sf ln(e^(3x-2))=ln(e^(x))`

With the previous property :

`\sf 3x-2=x`

Now let's substract x from both sides :

`\sf 3x-2-x=x-x\\2x-2=0`

Add 2 to both sides :

`\sf 2x-2+2=2\\2x=2`

Finally, let's divide both sides by 2 :

`\sf (2x)/(2) =(2)/(2)\\ \boxed{\sf x=1}`

Have a nice day ;)