Question
Write an equivalent exponential equation. \( \log _{3} 9=2 \)
Ask by Jimenez Knight. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The equivalent exponential equation is \( 3^2 = 9 \).
Solution
1. Recall the definition of a logarithm: if
\[
\log_a b = c,
\]
then it is equivalent to
\[
a^c = b.
\]
2. Given the logarithmic equation
\[
\log_{3} 9 = 2,
\]
we can convert it to its exponential form by letting \( a = 3 \), \( c = 2 \), and \( b = 9 \).
3. The equivalent exponential equation is therefore:
\[
3^2 = 9.
\]
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Simplify this solution Mind Expander
To express the logarithmic equation \( \log_{3} 9 = 2 \) in an equivalent exponential form, we can convert the log base to an exponent. This means that the base (3) raised to the power of the result (2) equals the argument (9). So we write: \[ 3^{2} = 9 \] This tells us that raising 3 to the power of 2 indeed gives us 9, confirming that our conversion is accurate! Happy learning!
