Questions: Use the like bases property to solve the equation 2^x=16 x=

Use the like bases property to solve the equation 2^x=16 x=
Transcript text: Use the like bases property to solve the equation \[ 2^{x}=16 \] \[ \boldsymbol{x}= \] Question Help: Video Submit Question
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Solution

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Solution Steps

To solve the equation \(2^x = 16\) using the like bases property, we need to express 16 as a power of 2. Since \(16 = 2^4\), we can set the exponents equal to each other and solve for \(x\).

Step 1: Rewrite the Equation

We start with the equation: \[ 2^x = 16 \]

Step 2: Express 16 as a Power of 2

Next, we express 16 as a power of 2: \[ 16 = 2^4 \] Thus, we can rewrite the equation as: \[ 2^x = 2^4 \]

Step 3: Set the Exponents Equal

Since the bases are the same, we can set the exponents equal to each other: \[ x = 4 \]

Final Answer

The solution to the equation is: \[ \boxed{x = 4} \]

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