which expressions are equivalent to ln x + 2 ln 5 + ln 1? check all that apply. 2 ln 5x ln (x + 26) ln 25x +…

which expressions are equivalent to ln x + 2 ln 5 + ln 1? check all that apply. 2 ln 5x ln (x + 26) ln 25x + ln 1 ln 25x done

which expressions are equivalent to ln x + 2 ln 5 + ln 1? check all that apply. 2 ln 5x ln (x + 26) ln 25x + ln 1 ln 25x done

Answer

Explanation:

Step1: Apply logarithm properties

Use the power - rule $n\ln a=\ln(a^{n})$ and the product - rule $\ln a+\ln b = \ln(ab)$. We know that $2\ln5=\ln(5^{2})=\ln25$ and $\ln1 = 0$. So, $\ln x+2\ln5+\ln1=\ln x+\ln25 + 0$.

Step2: Combine logarithms

By the product - rule $\ln x+\ln25=\ln(25x)$. Also, $\ln(25x)+\ln1=\ln(25x\times1)=\ln(25x)$ since $\ln1 = 0$.

Answer:

C. $\ln 25x+\ln 1$, D. $\ln 25x$