Question

1. solve for x.

$2^x = 25$
solve for x.
\\(\bigcirc\\) a. \\(x = \boxed{}\\)
(do not round until the final answer. then round to four decimal places as needed. use a comma to separate answers as needed.)
\\(\bigcirc\\) b. there is no solution.

Explanation:

Step1: Apply logarithm to both sides

Take $\log_2$ of both sides: $\log_2(2^x) = \log_2(25)$

Step2: Simplify left-hand side

Use $\log_a(a^x)=x$: $x = \log_2(25)$

Step3: Convert to common logarithm

Change base formula: $x = \frac{\log(25)}{\log(2)}$

Step4: Calculate and round

Compute value, round to 4 decimals: $x \approx \frac{1.39794}{0.30103} \approx 4.6439$

Answer:

A. $x = 4.6439$