Solve 3 In 2x =3 + In 27
I am assuming you mean $\displaystyle \ln$ and not $\displaystyle \text{In}$. We are given:
$\displaystyle 3\ln(2x)=3+\ln(27)$
I would rewrite this as:
$\displaystyle 3\ln(2x)=3+\ln(3^3)$
so that we may use the property $\displaystyle \log_a(b^c)=c\cdot\log_a(b)$ to then rewrite the equation as:
$\displaystyle 3\ln(2x)=3+3\ln(3)$
Next, divide through by 3:
$\displaystyle \ln(2x)=1+\ln(3)$
Next, use the fact that $\displaystyle \ln(e)=1$ to write:
$\displaystyle \ln(2x)=\ln(e)+\ln(3)$
To finish now, on the right use the property $\displaystyle \log_a(b)+\log_a(c)=\log_a(bc)$, then equate the resulting arguments, then solve for $\displaystyle x$.