Expand the Logarithmic Expression log base 2 of 16

Problem

(log_2)(16)

Solution

1. Identify the base and the argument of the logarithmic expression.

2. Rewrite the argument 16 as a power of the base 2

16=2

3. Substitute the power back into the logarithmic expression.

(log_2)(2)

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

4*(log_2)(2)

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

4⋅1=4

Final Answer

(log_2)(16)=4

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