Question

1. solve for \\(x\\) : \\(2^{2x+1} = 5\\)

Explanation:

Convert exponential equation to logarithmic form

$$ 2^{2x+1} = 5 \implies 2x + 1 = \log_2(5) $$

Isolate the variable term

$$ 2x = \log_2(5) - 1 $$

Solve for x

$$ x = \frac{\log_2(5) - 1}{2} $$

Answer:

\(x = \frac{\log_2(5) - 1}{2}\)