The dimensions of a, b, and c in y=a log(ab)/(c+d) are the same as y, dimensionless, and the same as y respectively, assuming y represents a physical quantity with dimensions.
To find the dimensions of a, b, and c in the given logarithmic equation y=a log(ab)/(c+d), we can use dimensional analysis. Dimensional analysis is a technique in physics where we check the consistency of different terms in an equation by ensuring that both sides of an equation have the same dimension. The dimension of y must be the same as the dimension on the right-hand side of the equation.
Since logarithms are dimensionless, the dimension of a will also be the same as y. The term ab under the log indicates that b must be dimensionless because you cannot take a logarithm of a quantity that has dimension. The denominator c+d implies that c and d must have the same dimension to be added together, which is also the dimension of y and a.
So, the dimensions of a, b, and c are M1L2T-2 (assuming y has this dimension), dimensionless, and M1L2T-2 respectively if we assume y represents a physical quantity like work or energy.