Evaluate log base 2 of 0.5

Problem

(log_2)(0.5)

Solution

1. Convert the decimal 0.5 into a fraction.

0.5=1/2

2. Rewrite the fraction as a power of 2 using the rule for negative exponents.

1/2=2(−1)

3. Substitute the power back into the logarithmic expression.

(log_2)(2(−1))

4. Apply the logarithm power rule (log_b)(bx)=x

(log_2)(2(−1))=−1

Final Answer

(log_2)(0.5)=−1

Want more problems? Check here!