Answered

which expressions are equivalent to the one below? check all that apply.


log3 81 + log3 81

Alog3 6561
Blog3(3^8)
C8
Dlog 6561

Please help me!!!!

Verified Answer :

Julik

\(\log_a(x) +\log_a(y) =\log_a(x\times y) \\ \\ \log_3(81)+\log_3(81)=\log_3(81\times81) =\log_3(6561)\)
A. log3 6561
\(\log_3(6561)=log_3(3^8)=8 \\\)
В.  log3 (3^8)
С. 8

Answer:

Option A , B and C are correct

Step-by-step explanation:

Using the logarithmic rules:

\(\log_b m + \log_b n = \log_b (mn)\)

\(\log_b b^m = m\)

Given the expression:

\(\log_3 81+ \log_3 81\)

Apply the logarithmic rules:

\(\log_3 (81 \cdot 81)\)             ....[1]

⇒\(\log_3 6561\)

[1] ⇒

\(\log_3 (81 \cdot 81)\)

We can write this as:

\(\log_3 (3^4 \cdot 3^4) = \log_3 (3^8)\)

apply the logarithmic rules we get;

\(\log_3 3^8 = 8\)

Therefore, the expression are equivalent to the \(\log_3 81+ \log_3 81\) are:

\(\log_3 6561\)

\(\log_3 (3^8)\) and

8

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