Pritchard Ruiz
10/14/2023 · Middle School
\( 1 \leftarrow \quad \) Solve the following exponential equatio \[ 3^{x-1}=434 \]
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Tutor-Verified Answer
Step-by-step Solution
Solve the equation \( 3^{x-1}=434 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(3^{x-1}=434\)
- step1: Take the logarithm of both sides:
\(\log_{3}{\left(3^{x-1}\right)}=\log_{3}{\left(434\right)}\)
- step2: Evaluate the logarithm:
\(x-1=\log_{3}{\left(434\right)}\)
- step3: Move the constant to the right side:
\(x=\log_{3}{\left(434\right)}+1\)
The solution to the exponential equation \(3^{x-1}=434\) is \(x=\log_{3}{(434)}+1\).
Quick Answer
\( x=\log_{3}{(434)}+1 \)
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