Question

solve the following elementary exponential equation.
$2^x - 16 = 0$
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4 points
$x = $

Explanation:

Step1: Isolate the exponential term

We start with the equation \(2^x - 16 = 0\). To isolate the exponential term \(2^x\), we add 16 to both sides of the equation.

$$2^x - 16 + 16 = 0 + 16$$

Simplifying both sides, we get:

$$2^x = 16$$

Step2: Express 16 as a power of 2

We know that \(16 = 2^4\) because \(2\times2\times2\times2 = 16\). So we can rewrite the equation as:

$$2^x = 2^4$$

Step3: Solve for \(x\)

Since the bases are the same and the exponential function \(y = 2^x\) is one - to - one (if \(a^m=a^n\), then \(m = n\) for \(a>0,a
eq1\)), we can set the exponents equal to each other. So \(x = 4\).

Answer:

\(x = 4\)