we have the expression
[tex]\text{log (P}-Q)=\log P-\log Q[/tex]
Applying properties of log right side
[tex]\text{log (P}-Q)=\log (\frac{P}{Q})[/tex]
Equate the numbers inside the parenthesis
[tex]P-Q=\frac{P}{Q}_{}[/tex]
Solve for P
[tex]P-\frac{P}{Q}=Q[/tex][tex]P\lbrack1-\frac{1}{Q}\rbrack=Q[/tex][tex]P=\frac{Q}{\lbrack1-\frac{1}{Q}\rbrack}[/tex]
Simplify
[tex]P=\frac{Q^2}{Q-1}[/tex]
