IB Maths AI HL Sl 1 5 Integer Exponents and Logarithms Topic Practice

This question is about applying ideas from logarithms, calculus and probability to an unfamiliar mathematical theory called information theory.
Claude Shannon developed a mathematical theory called information theory to measure the information gained when random events occur. He defined the information, I, that is gained when an event with probability p occurs as

where $0<p \leq 1$. For example, no information is gained ( I=0 ) when an event is certain to $\operatorname{occur}(p=1)$.

When a coin is flipped, the outcome is either heads or tails. The coin may be biased. Let p be the probability of the outcome being heads.

Find, in terms of p, the information gained when the outcome is tails.