1. **State the problem:** Logan has read 180 pages, which is 75% of the total pages $t$ in the e-book. We need to find $t$. 2. **Write the equation:** Since 75% means 75 out of 100, the fraction of pages read is $\frac{75}{100} = \frac{3}{4}$. The equation relating pages read to total pages is: $$\frac{180}{t} = \frac{3}{4}$$ 3. **Solve for $t$:** Cross-multiply to get: $$180 \times 4 = 3 \times t$$ $$720 = 3t$$ 4. **Isolate $t$ by dividing both sides by 3:** $$\frac{720}{\cancel{3}} = \frac{3t}{\cancel{3}}$$ $$240 = t$$ 5. **Answer:** The total number of pages in the e-book is $\boxed{240}$ pages. This means Logan has read three-quarters of 240 pages, which is 180 pages.