Question

Which expressions are equivalent to log4(1/4x^2)

Answer 1

The equivalent of log₄(1/4 x²) is log₄ 1 /4 + log₄ x²

log₄(1/4 x²)

Rule of logarithm

• logₐ(b)² = 2logₐb

Therefore,

log₄(1/4 x²) = log₄(1/2 x)²

Then,

log₄(1/2 x)² = 2 log₄ 1/2 x

or

Using logarithm rule,

• logₐb + logₐc = logₐbc

Therefore,

log₄(1/4 x²) = log₄ 1 /4 + log₄ x²

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