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log_(8)2=

$\log _{8} 2=$

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Relationship between squares and square roots

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Q.

\log _{8} 2=

Finding the Logarithm Base: We want to find the value of $\log_{8}2$ . This means we are looking for the exponent that $8$ must be raised to in order to get $2$ .
Expressing $8$ as a Power of $2$ : We can express $8$ as a power of $2$ , since $8$ is $2$ cubed ( $2^3$ ). This will help us to simplify the logarithm.
Rewriting the Logarithm: Now we rewrite the logarithm using the fact that $8$ is $2^3$ : $\log_{(2^3)} 2$ .
Simplifying Using Logarithm Property: Using the property of logarithms that $\log_{a^b}c = \frac{1}{b} \cdot \log_a(c)$ , we can simplify our expression to $\frac{1}{3} \cdot \log_{2}2$ .
Determining the Value of $\log(2)2$ : We know that $\log_{2}2$ is $1$ , because $2$ raised to the power of $1$ is $2$ .
Calculating the Final Answer: Multiplying $\frac{1}{3}$ by $1$ gives us the final answer: $\frac{1}{3} \times 1 = \frac{1}{3}$ .

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