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It is perfectly fine to visit a Chinese friend on an L (tourist) visa. To obtain the visa, your friend should write a letter of invitation and send it to you. You should submit it with your visa application.
According to the visa application instructions, the invitation letter should include:
The invitation letter should contain:
a. Information on the applicant (full name, gender, date of birth, etc.)
b. Information on the planned visit (arrival and departure dates, place(s) to be visited, etc.)
c. Information on the inviting entity or individual (name, contact telephone number, address, official stamp, signature of the legal representative or the inviting individual)
See the instructions for additional documents that you must provide.