Question
Write the given exponential equations in logarithmic form. \[ \begin{array}{ll}5^{x}=y\end{array} \]
Ask by Murphy Nguyen. in the United States
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The logarithmic form of \( 5^{x} = y \) is \( \log_{5}(y) = x \).
Solution
To convert the exponential equation \( 5^{x} = y \) into logarithmic form, we follow the definition of logarithms. The general form of converting an exponential equation \( a^{b} = c \) into logarithmic form is:
\[
\log_{a}(c) = b
\]
In this case, we have:
- \( a = 5 \)
- \( b = x \)
- \( c = y \)
Thus, the logarithmic form of the equation \( 5^{x} = y \) is:
\[
\log_{5}(y) = x
\]
So, the final answer is:
\[
\log_{5}(y) = x
\]
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Simplify this solution Extra Insights
To convert the exponential equation \(5^{x} = y\) into logarithmic form, we can rephrase it as "the logarithm of \(y\) with base \(5\) equals \(x\)." So, we write it as: \[ \log_{5}(y) = x \] This transformation showcases the relationship between the base, the exponent, and the result. Just think of it as flipping the equation around to express it in a different, yet equally valid, mathematical language! Now you can easily solve for \(x\) using logarithms whenever you're dealing with exponential equations! Remember, it's all about changing perspectives!
