Question
Write the equation in exponential form. \( \log _{3} 81=4 \) \( [?]=\square \)
Ask by Potter Evans. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 3^{4} = 81 \)
Solution
To convert the logarithmic equation \( \log_{3} 81 = 4 \) into its exponential form, you can use the definition of a logarithm:
\[
\log_{b} a = c \quad \text{is equivalent to} \quad b^{c} = a
\]
Applying this to your equation:
\[
\log_{3} 81 = 4 \quad \Rightarrow \quad 3^{4} = 81
\]
**Exponential Form:**
\[
3^{4} = 81
\]
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Simplify this solution Bonus Knowledge
To convert the logarithmic equation \( \log_{3} 81 = 4 \) into exponential form, we can use the definition of a logarithm. This tells us that the base (which is 3) raised to the power of the result (which is 4) gives us the argument (which is 81). So, we write it as: \[ 3^{4} = 81 \] This means that if you take 3 and multiply it by itself four times (which is \( 3 \times 3 \times 3 \times 3 \)), you indeed get 81. So, we have \( [3^{4} = 81] = \square \).
