Questions: Solve the following equation for (x). [ 2^3 x=2^6 x= ] (Type an integer or a simplified fraction.)

Solve the following equation for (x). [ 2^3 x=2^6 x= ] (Type an integer or a simplified fraction.)
Transcript text: LTI Launch Quiz Solve the following equation for $x$. \[ \begin{array}{l} 2^{3 x}=2^{6} \\ x=\square \end{array} \] $\square$ (Type an integer or a simplified fraction.)
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Solution

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Solution Steps

To solve the equation \(2^{3x} = 2^6\), we can use the property of exponents that states if the bases are the same, then the exponents must be equal. Therefore, we can set the exponents equal to each other and solve for \(x\).

Step 1: Set the Exponents Equal

Given the equation \(2^{3x} = 2^6\), we can set the exponents equal to each other because the bases are the same: \[ 3x = 6 \]

Step 2: Solve for \(x\)

To solve for \(x\), divide both sides of the equation by 3: \[ x = \frac{6}{3} = 2 \]

Final Answer

\[ \boxed{x = 2} \]

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