Expand the Logarithmic Expression log base 2 of 32

Problem

(log_2)(32)

Solution

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

2. Rewrite the argument 32 as a power of the base 2

32=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)

5*(log_2)(2)

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

5*(1)=5

Final Answer

(log_2)(32)=5

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