Question 147814
Your thinking is correct.
However your calculations are not.
{{{P=12+50*ln(x)}}}
{{{P=12+50*ln(4)}}}
{{{P=12+50*1.386294}}}
I'm not sure where the 3.91 comes in other than from ln(50)=3.91.
That's your mistake. 
{{{P=12+50*1.386294}}}
{{{P=12+69.31}}}
{{{P=81.31}}}
And the same for the second part.
The thinking was clear but the calculation had mistakes. 
{{{90=12+50*ln(x)}}}
Solve for x.
{{{78=50*ln(x)}}} Subtract 12 from both sides.
{{{1.56=ln(x)}}} Divide both side by 50.
{{{x=4.76}}} Use the inverse of the natural log function ({{{e^x}}}).