With a bit of help from Overloading Macro on Number of Arguments you could do it something like this.
#define LOG_VARIABLES( FORMAT, ...) NSLog( FORMAT, __VA_ARGS__ )
#define STR(X) #X
#define VAL(X) @(STR(X)), X
#define LOG1( FORMAT, A )                LOG_VARIABLES( FORMAT, VAL( A ) )
#define LOG2( FORMAT, A, B )             LOG_VARIABLES( FORMAT, VAL( A ), VAL( B ) )
#define LOG3( FORMAT, A, B, C )          LOG_VARIABLES( FORMAT, VAL( A ), VAL( B ), VAL( C ) )
#define LOG4( FORMAT, A, B, C, D )       LOG_VARIABLES( FORMAT, VAL( A ), VAL( B ), VAL( C ), VAL( D ) )
#define LOG5( FORMAT, A, B, C, D, E )    LOG_VARIABLES( FORMAT, VAL( A ), VAL( B ), VAL( C ), VAL( D ), VAL( E ) )
#define LOG6( FORMAT, A, B, C, D, E, F ) LOG_VARIABLES( FORMAT, VAL( A ), VAL( B ), VAL( C ), VAL( D ), VAL( E ), VAL( F ) )
#define GET_MACRO( FORMAT, _1, _2, _3, _4, _5, _6, NAME, ... ) NAME
#define LOG_X(FORMAT,...) GET_MACRO(_0, ##__VA_ARGS__, LOG6, LOG5, LOG4, LOG3, LOG2, LOG1 )(FORMAT,__VA_ARGS__)
int main ( int argc, const char * argv [] ) {
    @autoreleasepool
    {
        // insert code here...
        NSLog(@"Hello, World!");
        NSString * a = @"aa";
        NSString * b = @"bb";
        NSString * c = @"cc";
        NSString * d = @"dd";
        NSString * e = @"ee";
        NSString * f = @"ff";
        LOG_X(@"%@:%@",a);
        LOG_X(@"%@:%@ and %@:%@",a,b);
        LOG_X(@"%@:%@ and %@:%@ and %@:%@",a,b,c);
        LOG_X(@"%@:%@ and %@:%@ and %@:%@ and %@:%@",a,b,c,d);
        LOG_X(@"%@:%@ and %@:%@ and %@:%@ and %@:%@ and %@:%@",a,b,c,d,e);
        LOG_X(@"%@:%@ and %@:%@ and %@:%@ and %@:%@ and %@:%@ and %@:%@",a,b,c,d,e,f);
    }
    return 0;
}
Let me hasten to add that there are probably better ways to accomplish what you are trying to do and this is just a sample that only works to 6 arguments, but you get the idea ... also, I started out with your LOG_VARIABLES but along the way it morphed into LOG_X.