Expand the logarithm log4(w64)

Question

log
4
⁡
(
𝑤
64
)
.(1 point)
Responses

log4w−3
log
4
⁡
𝑤
−
3
logarithm subscript 4 baseline w minus 3

log4w3
log
4
⁡
𝑤
3
Start Fraction logarithm subscript 4 baseline w over 3 End Fraction

log4(w−3)
log
4
⁡
(
𝑤
−
3
)
logarithm subscript 4 baseline left parenthesis w minus 3 right parenthesis

log4(w3)

Answer 1

To expand the logarithm \( \log_4(w^{64}) \), we can use the logarithmic property that states:

\[ \log_b(a^c) = c \cdot \log_b(a) \]

Applying this property to \( \log_4(w^{64}) \):

\[ \log_4(w^{64}) = 64 \cdot \log_4(w) \]

Therefore, the expanded form of \( \log_4(w^{64}) \) is:

\[ 64 \log_4(w) \]

Since none of the provided options directly match this result, it seems the answers provided do not properly address the expansion of \( \log_4(w^{64}) \).

If you would like me to clarify or assist further, please let me know!