Today in Precalculus Go over homework Notes: Solving Log Equations Homework Quiz Friday, January 10

Steps to Solving Log Equations If there is only one term with a log or LN term, isolate it. If there is more than one term on either side with a log term, use properties of logs to condense it to one term. Convert to an exponent (if there is ONE log term on each side, can cancel the log) Use algebra to solve for unknown. Check for extraneous solutions by substituting solutions into original equation and verify no negatives values in log term.

Example lnx = 8 e 8 = x x = Check: ln =8 so x = is the answer

Example 7 + 3log 6 2x = 9 3log 6 2x = 2 x = 1.65 Check: 7 + 3log 6 2(1.65) 7 + 3log which is positive, so answer is x = 1.65

Example log(4x + 2) – log(x – 1) = 1 10x – 10 = 4x + 2 x = 2 Check: both log terms still positive, so x=2 is the answer

Example ln(x – 2) + ln(2x – 3) = 2lnx ln(x – 2)(2x – 3) = lnx 2 ln(2x 2 – 7x + 6) = lnx 2 2x 2 – 7x + 6 = x 2 x 2 – 7x + 6 = 0 (x – 6)(x – 1) = 0 x – 6 = 0 x – 1 = 0 x=6 x = 1 Check: ln(1 – 2) is ln(-1) so 1 is an extraneous solution, only answer is x = 6

Example logx 2 = = x = x 2 x = -10, 10

Homework Pg 331: 7-10, 17,18,25-28,35-38 Quiz: Friday, January 10