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

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.

1. Recognize that 128 can be written as \(2^7\).
2. Set the exponents equal to each other: \(x = 7\).

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

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