Solve this equation
$\displaystyle e^{3x}-2e^{-x} = 0$
I solved in this way, but i dont know if it is correct.
$\displaystyle e^{3x}-2e^{-x} = 0$
$\displaystyle e^{3x} = e^{-x} + e^{-x}$
$\displaystyle 3x + 2x = 0$
$\displaystyle x = 0$??
Solve this equation
$\displaystyle e^{3x}-2e^{-x} = 0$
I solved in this way, but i dont know if it is correct.
$\displaystyle e^{3x}-2e^{-x} = 0$
$\displaystyle e^{3x} = e^{-x} + e^{-x}$
$\displaystyle 3x + 2x = 0$
$\displaystyle x = 0$??
You started with $\displaystyle e^{{\color{red}3}x}-2e^{-x}=0$
When I multiplied through by $\displaystyle e^x$, it became:
$\displaystyle e^{{\color{red}4}x}-2=0$
The functions are not the same, because I've multiplied through by $\displaystyle e^x$ which is variable. But when you multiply 0 by $\displaystyle e^x$, the value is still 0 - nothing changes, so the intercept doesn't change.
This is correct but it's not clear that this helps.
This does not follow at all!$\displaystyle 3x + 2x = 0$
Did you not consider checking that answer? If x= 0 then both $\displaystyle e^{3x}$ and $\displaystyle e^x$ are $\displaystyle e^0= 1$$\displaystyle x = 0$??
Do you beieve that 1- 2= 0?