Evaluate log base 2 of 16^23

Problem

(log_2)(16^23)

Solution

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

(log_2)(16^23)=23*(log_2)(16)

2. Rewrite the base of the argument to match the base of the logarithm by expressing 16 as a power of 2

16=2^4

3. Substitute the power back into the logarithmic expression.

23*(log_2)(16)=23*(log_2)(2^4)

4. Simplify the logarithm using the identity (log_b)(b^k)=k

(log_2)(2^4)=4

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

23×4=92

Final Answer

(log_2)(16^23)=92

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