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

Use properties of exponents to find the value of log8 1. (1 point)
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1/8
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Transcript text: Use properties of exponents to find the value of $\log _{8} 1$. (1 point) 1 $\frac{1}{8}$ 8 0
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Solution

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Solution Steps

To find the value of log81\log_{8} 1, we use the property of logarithms that states logba=c\log_{b} a = c if and only if bc=ab^c = a. In this case, we are looking for the value of cc such that 8c=18^c = 1. Since any number raised to the power of 0 is 1, the value of log81\log_{8} 1 is 0.

Step 1: Understanding the Logarithm

We need to find the value of log81\log_{8} 1. By the definition of logarithms, logba=c\log_{b} a = c means that bc=ab^c = a. Here, we want to determine cc such that 8c=18^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: 80=1 8^0 = 1 This implies that c=0c = 0.

Step 3: Conclusion

Thus, we find that: log81=0 \log_{8} 1 = 0

Final Answer

0\boxed{0}

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