how many ways can you rewrite the expression log 4 ​60?

An infinite number of ways.......here are a couple

log₄ (60)  = log₄ (20 * 3)  = log₄ (20) + log₄ (3)

log₄ (60)  = log₄ (15 * 4)  = log₄ (15) + log₄ (4)  = log₄ (15) + 1