how do I write this logarithm in expanded form?

Question

log₄ (c⁶d³f⁷)

Answer 1

log₄ (c⁶d³f⁷)

To expand, you need to use two log properties. The first is log(ab) = log(a) + log(b):

log₄ (c⁶d³f⁷) = log₄(c⁶) + log₄(d³) + log₄(f⁷)

The second property is log(a^b) = b·log(a):

log₄(c⁶) + log₄(d³) + log₄(f⁷) = 6·log₄(c) + ... You finish the last two terms.