Questions: Solve the exponential equation by expressing each side as a power of the 8^x = 16 The solution set is (Simplify your answer.)

Solution Steps

We start with the exponential equation \(8^x = 16\). We express both sides as powers of \(2\): \[ 8 = 2^3 \quad \text{and} \quad 16 = 2^4 \] Thus, we can rewrite the equation as: \[ (2^3)^x = 2^4 \]

Using the power of a power property, we simplify the left side: \[ 2^{3x} = 2^4 \]

Since the bases are the same, we can set the exponents equal to each other: \[ 3x = 4 \]

To find \(x\), we divide both sides by \(3\): \[ x = \frac{4}{3} \]

Final Answer