Questions: Use the like bases property to solve the equation 2^x = 128 x = □

Use the like bases property to solve the equation 2^x = 128 x = □
Transcript text: Use the like bases property to solve the equation \[ \begin{array}{l} 2^{x}=128 \\ x=\square \end{array} \] Question Help: Video Message instructor
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Solution

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Solution Steps

To solve the equation \(2^x = 128\), we need to express 128 as a power of 2. Once we do that, we can equate the exponents since the bases are the same.

Solution Approach
  1. Recognize that 128 can be written as \(2^7\).
  2. Set the exponents equal to each other: \(x = 7\).
Step 1: Express 128 as a Power of 2

We need to express 128 as a power of 2. We know that: \[ 128 = 2^7 \]

Step 2: Equate the Exponents

Given the equation \(2^x = 128\), we can substitute \(128\) with \(2^7\): \[ 2^x = 2^7 \]

Since the bases are the same, we can equate the exponents: \[ x = 7 \]

Final Answer

\[ \boxed{x = 7} \]

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