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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

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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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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!

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