Respuesta :

altavistard
use the basic rule of logs for multiplication:

log a + log b = log a*b

Here you are adding two logs to the base 2, and your result will also be a log to the base 2.

log to the base 2 of 6    PLUS   log to the base 2 of 7   results in:
"log to the base 2 of 6*7," or "log to the base 2 of 42."

Answer:  The correct option is (C) [tex]\log_242.[/tex]

Step-by-step explanation:  We are given to express the following logarithmic expression as a single logarithm :

[tex]E=\log_26+\log_27~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(I)[/tex]

We will be using the following logarithmic property :

[tex]\log_ab+\log_ac=\log_a(bc)[/tex]

So, from expression (i), we get

[tex]E=\log_26+\log_7=\log_2(6\times 7)=\log_242.[/tex]

Thus, the required single logarithm is [tex]\log_242.[/tex]

Option (C) is CORRECT.

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