Questions: Solve the following exponential equation. 2^x=3 Select the correct choice below and, if necessary, fill in the answer box. A. The solution is (Round to four decimal places as needed. Use a comma to separate answers as needed.) B. The solution is not a real number.

Solution Steps

To solve the exponential equation \( 2^{x} = 3 \), we first convert it to logarithmic form: \[ x = \log_{2}(3) \]

Using the change of base formula, we can express \( \log_{2}(3) \) in terms of common logarithms (base 10): \[ x = \frac{\log(3)}{\log(2)} \]

Calculating the value gives us: \[ x \approx 1.5849625007211563 \] Rounding this to four decimal places, we find: \[ x \approx 1.585 \]

Final Answer