The binary operation : R × R → R is defined as ab = 2a + b. Find (2*3)*4.

Since ab = 2a + b
Put a = 2 and b = 3 in ab = 2a + b as shown below:
23 = 2(2) + 3 = 4 + 3 = 7
We have to find (23)4 that is to find 74.
Now put a = 7 and b = 4 in ab = 2a + b as shown below:
74 = 2(7) + 4 = 14 + 4 = 18.
Hence (2*3)*4 = 18.