Question

question 10 of 10
which expressions are equivalent to the one below? check all that apply.
$log_{3} 3 + log_{3} 27$

a. $log 10$
b. $log_{3} 81$
c. $4$
d. $log_{3}(3^{4})$

Explanation:

Step1: Apply log addition rule

Using the property $\log_b a + \log_b c = \log_b (a \times c)$, we have $\log_3 3 + \log_3 27 = \log_3 (3 \times 27)$.
Calculate $3 \times 27 = 81$, so the expression becomes $\log_3 81$. (This checks option B)

Step2: Simplify $\log_3 81$

Since $81 = 3^4$, $\log_3 81 = \log_3 (3^4)$. (This checks option D)

Step3: Evaluate $\log_3 (3^4)$

Using the property $\log_b (b^x) = x$, we get $\log_3 (3^4) = 4$. (This checks option C)

Step4: Check option A

$\log 10$ (assuming base 10) is 1, which is not equal to our result, so A is incorrect.

Answer:

B. $\log_3 81$, C. 4, D. $\log_3(3^4)$