Write as an exponential equation. log_{4}256=4

Question

Complete the equivalent exponential equation ____=256 (Simplify your answer. Type in exponential form.)

Answer 1

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.