A few question i cannot solve and need some help on:
1)$\displaystyle ln(5x)-ln(3-2x)=1$
2)$\displaystyle ln(x)+ln(3x+1)=1$
3)$\displaystyle 8e^-x-e^x$
P.S
A few question i cannot solve and need some help on:
1)$\displaystyle ln(5x)-ln(3-2x)=1$
2)$\displaystyle ln(x)+ln(3x+1)=1$
3)$\displaystyle 8e^-x-e^x$
P.S
In that case multiply throughout by $\displaystyle e^x$
$\displaystyle 8-e^{2x}=2e^x$
Rearrange into the form $\displaystyle ax^2+bx+c=0$
$\displaystyle e^{2x}+2e^x-8=0$
Solve the quadratic (this one factorises) and then find x using the natural log. Remember that one solution will not be real.
I get solutions of
$\displaystyle x = ln(2)$ REAL
and
$\displaystyle x = ln(-4) = ln(4) + i\pi$ COMPLEX
You may only need the REAL solution