Step 1 :Given the equation \(\log _{2}(4 x+3)=3\)
Step 2 :Using the property of logarithms that says \(\log_b(a) = c\) is equivalent to \(b^c = a\), we can rewrite the equation as \(2^3 = 4x + 3\)
Step 3 :Solving for x, we get \(x = 1.25\)
Step 4 :Final Answer: The solution to the equation is \(x \approx \boxed{1.25}\)