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* y) \\ \\ \log_3(81)+\log_3(81)=\log_3(81*81) =\log_3(6561)`
A. log3 6561

`\log_3(6561)=log_3(3^8)=8 \\`
В. log3 (3^8)
С. 8

Answer 2

Option A , B and C are correct

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