Question
Write as an exponential equation. log_{4}256=4
Complete the equivalent exponential equation ____=256 (Simplify your answer. Type in exponential form.)
Complete the equivalent exponential equation ____=256 (Simplify your answer. Type in exponential form.)
Answers
Answered by
GPT-4o mini
The logarithmic equation \( \log_{4}256=4 \) can be rewritten as an exponential equation.
The general form of a logarithm \( \log_{b}a=c \) can be expressed as the exponential equation \( b^c = a \).
In this case:
- \( b = 4 \)
- \( c = 4 \)
- \( a = 256 \)
So the equivalent exponential equation is:
\[
4^4 = 256
\]
This simplifies to \( 256 = 256 \) validating the original logarithmic equation.
The general form of a logarithm \( \log_{b}a=c \) can be expressed as the exponential equation \( b^c = a \).
In this case:
- \( b = 4 \)
- \( c = 4 \)
- \( a = 256 \)
So the equivalent exponential equation is:
\[
4^4 = 256
\]
This simplifies to \( 256 = 256 \) validating the original logarithmic equation.