Questions: Use the definition of a logarithmic function to write the exponential equation as an equation involving a single logarithm 4^2=16 The equivalent equation involving a single logarithm is (Type an equation. Do not simplify.)

Use the definition of a logarithmic function to write the exponential equation as an equation involving a single logarithm

4^2=16

The equivalent equation involving a single logarithm is
(Type an equation. Do not simplify.)

Transcript text: Use the definition of a logarithmic function to write the exponential equation as an equation involving a single logarithm \[ 4^{2}=16 \] The equivalent equation involving a single logarithm is $\square$ (Type an equation. Do not simplify.)

Solution

Solution Steps

Step 1: Identify the Exponential Equation

The given exponential equation is

\[ 4^{2} = 16 \]

Step 2: Convert to Logarithmic Form

To convert the exponential equation to logarithmic form, we identify the base, exponent, and result:

Base: \(4\)
Exponent: \(2\)
Result: \(16\)

Using the definition of a logarithm, we can express the equation as:

\[ \log_{4}(16) = 2 \]

Final Answer

The equivalent equation involving a single logarithm is

\[ \boxed{\log_{4}(16) = 2} \]

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