Question

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

log3 81 + log3 81

A. log3 6561
B. log3(3^8)
C. 8
D. log 6561

Please help me!!!!

Answer 1

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

Answer 2

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