Today in Precalculus Go over homework Notes: Solving Exponential Equations Homework

Steps to Solving Exponential Equations Isolate the term with the variable exponent using algebra. Take the log of both sides (or convert to a log equation) Use properties of logs Solve for the unknown.

Example 5x = 358 log5x =log358 xlog5=log358 x = 3.654

Example 3ex - 6 = 48 3ex = 54 ex = 18 lnex = ln18 x=ln18 x = 2.890

Practice

x = -1.839

2. 6e2x + 10 = 46 6e2x = 36 e2x = 6 2x = ln6 x = .896

3. 10e-x + 45 = 83 10e-x = 38 e-x = 3.8 -x = ln3.8 -x = 1.335 x = -1.335

ex + 2e-x = 3 ex + 2e-x – 3 = 0 ex(ex + 2e-x – 3 = 0) e2x – 3ex + 2e0 = 0 e2x – 3ex + 2= 0 (ex – 2)(ex – 1) = 0 ex = 1 ex = 2 x = ln1 x = ln2 x = 0, .693

x =( log10.099)/(log2) or x = (log-0.099)/(log2) x = 3.336 2x – 2-x = 10 2x – 2-x – 10 = 0 2x(2x– 2-x – 10 = 0) 22x – 10(2x)– 20 = 0 22x – 10(2x ) – 1 = 0 2x = 10.099 or 2x = -.099 x =( log10.099)/(log2) or x = (log-0.099)/(log2) x = 3.336

Homework Page 331: 1-6, 11-16, 29-33 Quiz Friday, January 8