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