Lambert Bowers
07/25/2024 · Senior High School
If \( \log _{3} x=8 \) find \( x \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To solve the equation \( \log_{3} x = 8 \), we can rewrite it in exponential form. The logarithmic equation states that \( x \) is the number that \( 3 \) must be raised to in order to get \( x \). Therefore, we can express this as:
\[
x = 3^8
\]
Now, we need to calculate \( 3^8 \):
\[
3^8 = (3^4)^2 = 81^2
\]
Calculating \( 81^2 \):
\[
81 \times 81 = 6561
\]
Thus, we find that:
\[
x = 6561
\]
Therefore, the value of \( x \) is
\[
\boxed{6561}
\]
Quick Answer
\( x = 6561 \)
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