Pregunta
Write the equation in its equivalent logarithmic form. \( 3^{2}=9 \) What is the equivalent logarithmic form of the equation?
Ask by Crawford Welch. in Saudi Arabia
Mar 09,2025
Solución de inteligencia artificial de Upstudy
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The equivalent logarithmic form is \( \log_{3}(9)=2 \).
Solución
1. Recall that the exponential equation \( b^x = y \) can be rewritten in logarithmic form as \( \log_b(y) = x \).
2. In the equation \( 3^2 = 9 \), the base is \( 3 \), the exponent is \( 2 \), and the result is \( 9 \).
3. Therefore, the equivalent logarithmic form is
\[
\log_{3}(9)=2
\]
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Simplifique esta solución Bonus Knowledge
The equivalent logarithmic form of the equation \( 3^{2} = 9 \) is \( \log_{3}(9) = 2 \). This means that when you take the logarithm of 9 to the base of 3, you'll get 2 - the exponent you need to raise 3 to in order to achieve 9! Understanding this transformation is like unraveling a secret code. Logarithms help you work with exponential growth in a way that’s easier to manage. They're crucial in various fields, from measuring sound intensity (decibels) to calculating pH levels in chemistry. Who knew math could be so dynamic?
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