Use the definition of a logarithmic function to write the logarithmic equation as an equation involving an exponent.

Question

log Subscript 4 Baseline Upper J equals Upper K
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Part 1
The equivalent exponential equation is
  
enter your response here.
​(Type an equation. Do not​ simplify.)

Answer 1

To convert the logarithmic equation \( \log_4 J = K \) into its equivalent exponential form, we use the definition of a logarithm. The definition states that if \( \log_b a = c \), then \( b^c = a \).

Applying this to your equation:

1. The base \( b \) is \( 4 \).
2. The exponent \( c \) is \( K \).
3. The result \( a \) is \( J \).

So, we can rewrite the logarithmic equation as:

\[ 4^K = J \]

This is the equivalent exponential equation.