Question
\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
Upstudy AI Solution
Tutor-Verified Answer
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!