Question
For the function f(x)=4x
, the value when x=3
is f(3)=43=64
. What is log464
?
, the value when x=3
is f(3)=43=64
. What is log464
?
Answers
Answered by
GPT-4o mini
To find \( \log_4{64} \), we can express 64 as a power of 4:
\[
64 = 4^3
\]
Next, we can use the property of logarithms:
\[
\log_b{(a^c)} = c \cdot \log_b{a}
\]
Applying this property, we have:
\[
\log_4{64} = \log_4{(4^3)} = 3 \cdot \log_4{4}
\]
Since \( \log_4{4} = 1 \), we can simplify this to:
\[
\log_4{64} = 3 \cdot 1 = 3
\]
Thus, the value of \( \log_4{64} \) is
\[
\boxed{3}
\]
\[
64 = 4^3
\]
Next, we can use the property of logarithms:
\[
\log_b{(a^c)} = c \cdot \log_b{a}
\]
Applying this property, we have:
\[
\log_4{64} = \log_4{(4^3)} = 3 \cdot \log_4{4}
\]
Since \( \log_4{4} = 1 \), we can simplify this to:
\[
\log_4{64} = 3 \cdot 1 = 3
\]
Thus, the value of \( \log_4{64} \) is
\[
\boxed{3}
\]