Question

question 5 of 10
which expressions are equivalent to the one below? check all that apply.
log(10⁵)

a. 5·log 10

b. 5·10

c. 5

d. 1

Explanation:

Step1: Apply Log Power Rule

The power rule of logarithms states that $\log(a^b) = b \cdot \log(a)$. For $\log(10^5)$, we can apply this rule: $\log(10^5) = 5 \cdot \log(10)$. So option A is equivalent.

Step2: Evaluate $\log(10)$

We know that for the common logarithm (base 10), $\log_{10}(10) = 1$. So $5 \cdot \log(10) = 5 \cdot 1 = 5$. Thus option C is also equivalent. Option B is $5 \cdot 10 = 50$, which is not equal to $\log(10^5)$ (which is 5), and option D is 1, which is not equal to 5.

Answer:

A. $5 \cdot \log 10$, C. $5$