How to write a equation that x*(2^(y/x)-1) in CVX

hello, i want to know how to write a equation that x*(2^(y/x)-1) in CVX, and x,y>=0. This equation has exists in constraint and objective function simultaneously.
This equation should be jointly convex in x,y, it has been proved in some papers, very appreciate for your help.

x*(2^(y/x)-1) = x*exp(y*log(2)/x) - x

x*exp(y*log(2)/x can be replaced by a variable z and the constraint
{y*log(2),x,z} == exponential(1)

So the variable z is declared, x*(2^(y/x)-1) is replaced by z-x, and the constraint {y*log(2),x,z} == exponential(1) is added.

Thanks for your reply!
However, i rewrote program and i found a another problem
Here is my code:

    variable x
    variable y
    minimize( x*exp(y*log(2)*inv_pos(x)) - x )

This is not my original problem, but it is an important part of it, and here is error information:
Disciplined convex programming error:
Cannot perform the operation: {real affine} .* {convex}

You did not follow my instructions.

variables x y z
{y*log(2),x,z} == exponential(1)