Find the exact value of log base 2 of one sixteenth.

1. Set the logarithm equal to x, so log base 2 of one sixteenth equals x. 2. Convert to exponential form, giving 2 to the power x equal to one sixteenth. 3. Rewrite 16 as a power of 2 by doubling: 2, 4, 8, 16. 4. That takes four doublings, so 16 is 2 to the fourth. 5. A reciprocal flips the sign of the exponent, so one sixteenth is 2 to the power negative 4. 6. With the bases matching, the exponents must be equal, so x is negative 4. 7. Answering 4 ignores that the argument is a reciprocal rather than 16 itself. 8. Answering negative 8 doubles the exponent instead of counting the doublings. 9. Answering negative 16 reports the argument rather than the exponent. _Source: OpenStax Intermediate Algebra (CC BY 4.0), section 10.3 Evaluate and Graph Logarithmic Functions_