Evaluate log base 1/2 of 16

Problem

(log_1/2)(16)

Solution

1. Set the expression equal to x to represent the unknown value we are solving for.

(log_1/2)(16)=x

2. Rewrite in exponential form using the definition of a logarithm, where the base raised to the power of the result equals the argument.

(1/2)x=16

3. Express both sides with a common base of 2 to simplify the equation.

(2(−1))x=2

4. Apply the power of a power rule to the left side of the equation.

2(−x)=2

5. Equate the exponents since the bases are now identical.

−x=4

6. Solve for x by multiplying both sides by −1

x=−4

Final Answer

(log_1/2)(16)=−4

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