Use the power property to rewrite the log expression.
${\log }_2{(x+1)}^2$

• A. $x+1$
• B. $2\(\log\)_2\(\left\)(x+1\(\right\))$
• C. $\(\left\)(x+1\(\right\))\(\log\)_22$
• D. $2+\(\log\)_2\(\left\)(x+1\(\right\))$

Answer: (B)

Verified step by step guidance

1. Identify the given logarithmic expression: \(\log_2\left(x+1\right)^2\).
2. Recall the power property of logarithms, which states that \(\log_b\left(a^n\right) = n \log_b a\).
3. Apply the power property by moving the exponent 2 in front of the logarithm: \(\log_2\left(x+1\right)^2 = 2 \log_2\left(x+1\right)\).
4. Rewrite the expression explicitly showing the coefficient: \(2 \log_2\left(x+1\right)\).
5. This is the simplified form using the power property of logarithms.