How can i solve the problem

here is a simple case ,but cvx says i cant use a variable as denominater.i think i violate the DCP ruleset, but i dont know how to fix it, can anybody help me

cvx_begin
variables a
minimize(log(1+1/a)*a)
subject to
1<=a<=5
cvx_end

the errors are :
Disciplined convex programming error:
Cannot perform the operation: {positive constant} ./ {real affine}

出错 ./ (line 19)
z = times( x, y, ‘./’ );

出错 * (line 36)
z = feval( oper, x, y );

出错 / (line 15)
z = mtimes( x, y, ‘rdivide’ );

出错 Untitled2 (line 4)
minimize(log(1+1/a))*a

My original reply here was erroneous, because I misread the post.

but a is out of the log function.it would be clearer to rewrite log(1+1/a)a as alog(1+1/a). so i think log(1+1/a)*a can’t be rewritten as log(a+1).

Sorry, I misread the post.

Reformulate as
-rel_entr(a,a+1)

ok，i will try it. Thank you very much!

Unfortunately, that is concave, so it can be maximized, but not minimized in CVX.

thank you a lot! i got this one, but i have a more complex problem to solve.it’s kind similar to this simple problem. How can i solve this problem