Question

evaluate logarithms (level 2) unique id: 0060
score: 2.75/4 penalty: 0.25 off
question
what is the value of \\(\log_{7} \frac{1}{7}\\)?
answer attempt 1 out of 2

Explanation:

Step1: Recall logarithm property

We know that $\log_a a^x = x$ and also that $\frac{1}{a}=a^{-1}$. So, rewrite $\frac{1}{7}$ as $7^{-1}$.
So, $\log_{7}\frac{1}{7}=\log_{7}7^{-1}$.

Step2: Apply logarithm power rule

The power rule of logarithms states that $\log_a b^c = c\log_a b$. Here, $a = 7$, $b = 7$, and $c=- 1$. So, $\log_{7}7^{-1}=-1\times\log_{7}7$.

Step3: Evaluate $\log_{7}7$

We know that for any base $a$, $\log_a a = 1$. So, $\log_{7}7 = 1$. Then, $-1\times\log_{7}7=-1\times1=- 1$.

Answer:

-1