Expand the Logarithmic Expression log base 2 of 8

Problem

(log_2)(8)

Solution

1. Identify the base and the argument of the logarithmic expression. The base is 2 and the argument is 8

2. Rewrite the argument as a power of the base. Since 2×2×2=8 we can express 8 as 2

3. Substitute the power back into the expression to get (log_2)(2)

4. Apply the power rule for logarithms, which states (log_b)(xp)=p*(log_b)(x)

5. Simplify the resulting expression using the identity (log_b)(b)=1

Final Answer

(log_2)(8)=3

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