Questions: Re-write the equation in exponential form. log4(16)=2

Re-write the equation in exponential form. log4(16)=2
Transcript text: Re-write the equation in exponential form. \[ \log _{4}(16)=2 \]
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Solution

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Solution Steps

Step 1: Converting from logarithmic to exponential form

Given the logarithmic statement \(\log_{4} 16 = 2\), we use the fundamental identity that relates logarithms and exponentiation.

Step 2: Apply the conversion formula

The equivalent exponential form is obtained by recognizing that the base \(b\) raised to the power \(c\) equals \(a\).

Step 3: Perform the calculation

Thus, \(b^c = 4^{2} = 16\), which is the exponential form.

Final Answer: The exponential form of \(\log_{4} 16 = 2\) is \(b^c = 4^{2} = 16\).

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