Evaluate log base 2 of 1/32

Problem

(log_2)(1/32)

Solution

1. Identify the base and the argument of the logarithm. The base is 2 and the argument is 1/32

2. Rewrite the argument as a power of the base. Since 32=2 the fraction can be written using a negative exponent.

1/32=1/2

1/2=2(−5)

3. Substitute the power back into the logarithmic expression.

(log_2)(2(−5))

4. Apply the property of logarithms that states (log_b)(bx)=x

(log_2)(2(−5))=−5

Final Answer

(log_2)(1/32)=−5

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