Ok,
I want to try it. I use a Samsung tablet Galaxy A8 with the android version 13 (One UI Core 5.1.1). I will show, if I can commands with root-rights. My experience in root-things isn't good under this device type.

It does not matter what device or Android version you have. Both busybox and mount-utils have the same behaviour on all linux distros.

Hi,
my android has no root rights. Therefore termux cannot inherit them. I installed the tool fakeroot in termux. But mounting the image isn't possible, because no loop device is active (/dev/loopx). What can I do now ?

There is no other way than rooting the device for real. fakeroot will not work.

Ohh,
thank you for the discussion, although the result isn't satisfactorily. It is dangerous to try to root a Samsung device by special root images. The security design of the tablet is built in the manner, that a special electronic circuit of the hardware will be burnt. Only Samung itself can repair it.
How can I close the discussion ?

Best Regards
Rose