Evaluate log base 2 of (8)^33

Problem

(log_2)(8)

Solution

1. Apply the power property of logarithms, which states that (log_b)(xp)=p*(log_b)(x)

(log_2)(8)=33*(log_2)(8)

2. Rewrite the base of the argument as a power of 2, noting that 8=2

33*(log_2)(8)=33*(log_2)(2)

3. Evaluate the logarithm by applying the property (log_b)(bx)=x

33*(log_2)(2)=33⋅3

4. Multiply the remaining constants to find the final value.

33⋅3=99

Final Answer

(log_2)(8)=99

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