Solve the following equation ln(x^2-8x+13)=0

[A_Munk3y]

Homework Statement

Solve the following equation:
ln(x²-8x+13)=0

The Attempt at a Solution

not much luck with this one. i just learned this stuff and I am having problems with it'
Anyways, i got
ln(x²-8x+13=0
=>lnx²-ln8x+ln13=0
=>lnx²-ln8x=-ln13
=>ln(x²/8x)=-ln13
=>e^ln(x2/8x)=e^-ln13
=>x²/8x=e^-ln13

im just going to stop there cause i think I am going in the wrong direction

 

[Mentallic]

$$ln(a+b)\neq ln(a)+ln(b)$$

But rather,

$$ln(ab)=ln(a)+ln(b)$$

Firstly, take the exponential of both sides, since $$e^{ln(x)}=x$$

But also remember that you can only take the log of a positive number, so you might need to discard a value when you solve for x.

 

[A_Munk3y]

Oh, ok :)
I got it! Thank you

 

[Mentallic]

No problem