Questions: Use properties of exponents to find the value of log8 1. (1 point) 1 1/8 8 0

Transcript text: Use properties of exponents to find the value of $\log _{8} 1$. (1 point) 1 $\frac{1}{8}$ 8 0

Solution

Solution Steps

To find the value of $\log_{8} 1$, we use the property of logarithms that states $\log_{b} a = c$ if and only if $b^c = a$. In this case, we are looking for the value of $c$ such that $8^c = 1$. Since any number raised to the power of 0 is 1, the value of $\log_{8} 1$ is 0.

Step 1: Understanding the Logarithm

We need to find the value of $\log_{8} 1$. By the definition of logarithms, $\log_{b} a = c$ means that $b^c = a$. Here, we want to determine $c$ such that $8^c = 1$.

Step 2: Applying the Property of Exponents

We know that any number raised to the power of 0 equals 1. Therefore, we can conclude that: \[ 8^0 = 1 \] This implies that $c = 0$.

Step 3: Conclusion

Thus, we find that: \[ \log_{8} 1 = 0 \]