Questions: Solve for (x) [ (x+7)^5 / 3=32 x= ]

Solve for (x) [ (x+7)^5 / 3=32 x= ]
Transcript text: Solve for $x$ \[ \begin{array}{l} (x+7)^{5 / 3}=32 \\ x= \end{array} \]
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Solution

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Solution Steps

To solve for \( x \) in the equation \((x+7)^{5/3} = 32\), we can follow these steps:

  1. Isolate the term with the exponent by taking both sides of the equation to the power of \( \frac{3}{5} \).
  2. Subtract 7 from both sides to solve for \( x \).
Step 1: Isolate the Term with the Exponent

Given the equation: \[ (x + 7)^{5/3} = 32 \] To isolate \( x + 7 \), we take both sides of the equation to the power of \( \frac{3}{5} \): \[ (x + 7) = 32^{3/5} \]

Step 2: Calculate the Right-Hand Side

Calculate \( 32^{3/5} \): \[ 32^{3/5} \approx 8 \]

Step 3: Solve for \( x \)

Subtract 7 from both sides to solve for \( x \): \[ x = 32^{3/5} - 7 \] \[ x \approx 8 - 7 \] \[ x \approx 1 \]

Final Answer

\[ \boxed{x \approx 1} \]

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