Question
Solve the given equation for \( x \). \( 4^{\frac{z}{8}}=4 \) \( x=\square \)
Ask by Wagner Lambert. in the United States
Mar 13,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x=8 \)
Solution
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The Deep Dive
To solve the equation \( 4^{\frac{z}{8}} = 4 \), we can express \( 4 \) as \( 4^1 \). This gives us the equation: \[ 4^{\frac{z}{8}} = 4^1 \] Since the bases are the same, we can set the exponents equal to each other: \[ \frac{z}{8} = 1 \] To find \( z \), multiply both sides by 8: \[ z = 8 \] So, the solution for \( x \) is \( 8 \). \( x = 8 \)
