If me and my partner did not both sign the lease for my business¿is it valid?

Unless you told the landlord that the lease would not be valid until and unless your partner also signed it, it is valid, or at least the lack of your partner's signature does not invalidate it.  When you refer to your "partner", are you just employing shorthand, or have the two of you actually formed af separate partnership entity?  If the tenant is an entity, whether it be a partnership, llc, or even a corporation, the lease is valid against it because you were authorized to enter into the lease on its behalf (even if you didn't actually have authority, the landlord didn't know that and was entitled to rely on your apparent authority.)  If, however, your "partner" and yourself are acting as two individuals, the lease is valid against you because you signed it.  The landlord may have a tough time going after your partner for breach of the lease, and you might have a tough time going after him for his share of the rent, because he didn't sign the lease and (depending on its term) it may be the type of contract which is required to be in writing.  However, as between you and the landlord, the lease would be valid.