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\begin{tabular}{l} Write an equivalent exponential equation. \\ \( \qquad \log 10000=4 \) \\ \hline\end{tabular}

Ask by Logan Norris. in the United States
Mar 09,2025

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Answer

The equivalent exponential equation is \(10^4 = 10000\).

Solution

1. We start with the logarithmic equation: \[ \log 10000 = 4 \] 2. Recall the definition of the logarithm: \[ \log_a b = c \quad \Longleftrightarrow \quad a^c = b \] Here, the base \(a\) is assumed to be \(10\). 3. Using the definition, rewrite the equation in its exponential form: \[ 10^4 = 10000 \]

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Bonus Knowledge

The equivalent exponential equation for \( \log 10000 = 4 \) is \( 10^4 = 10000 \). This means that when you raise 10 to the power of 4, you get 10000. It’s a clear example of how logarithms and exponents are two sides of the same coin, helping to bridge our understanding of exponential relationships!

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