Question

solve the equation.
\\(\log_{4} 16 = 2x + 9\\)

the solution set is \\(\\{\quad\\}\\).
(type an integer or a simplified fraction. use a comma to separate answers as needed.)

Explanation:

Step1: Simplify the logarithm

Recall that \(\log_{a}a^{b}=b\). For \(\log_{4}16\), since \(4^{2} = 16\), we have \(\log_{4}16=\log_{4}4^{2}=2\). So the equation becomes \(2 = 2x+9\).

Step2: Solve for x

Subtract 9 from both sides: \(2 - 9=2x+9 - 9\), which simplifies to \(-7 = 2x\). Then divide both sides by 2: \(x=\frac{-7}{2}\).

Answer:

\(-\frac{7}{2}\)