Exponential and Logarithmic Functions - Sketching Logarithmic Functions and Solving Equations Graphically

The curve of \(y={{\log }_{a}}\left( 2x+b \right)+1\) passes through \(\left( \frac{3}{2},2 \right)\) and \(\left( \frac{93}{2},3 \right)\). Find the values of \(a\) and \(b\).

Hence, sketch the graphs of \(y={{\log }_{a}}\left( 2x+b \right)+1\), labelling the coordinates of axial intercepts and equations of asymptotes.