ADVANCED EXERCISES - Logarithms and Solving Equations

---

(1) Rewrite each expression so that there are no logs of products, quotients or powers.

1. ln (e^4x )
   
   
2. ln [(x² - 1) / (x-1)²], x > 1

( Click On HINT To Get Some Help , Click On SOLUTION To See The Answer )

(2) Solve each equation. In part d., solve for t.

1. ln(0.8x + 0.03) = 0.01
   
   
2. 0.25P₀ = P₀e^-0.4t (P₀ is a non-zero constant.)
   
   
3. log₂(log₃x) = 4
   
   
4. A = P(1 + r/n)^nt

( HINT , SOLUTION )

(3) Express as a power of e. Example: x² = e^ln(x2) = e^{2ln x}

1. x^1.4
2. x^x
3. 3^t

( HINT , SOLUTION )

---