Answer: The correct option is (D) [tex]\log_242.[/tex]
Step-by-step explanation: We are given to write the following logarithmic expression as a single logarithm :
[tex]E=\log_26+\log_27.[/tex]
We will be using the following property of logarithm :
[tex]\log_ab+\log_ac=\log_abc.[/tex]
For the given expression, we have
[tex]E\\\\=\log_26+\log_27\\\\=\log_2(6\times7)\\\\=\log_242.[/tex]
Thus, the required single logarithm is [tex]\log_242.[/tex]
Option (D) is CORRECT.
