D-10 Solving Log Equations Using Properties Notes
โ Equations in the form of ๐๐๐๐(๐ฅ) = ๐๐๐๐(๐ฆ)
Examples: Solve the equation for x. Round answers to 3 decimal places. a. ๐๐๐13(2๐ฅ) = ๐๐๐13(๐ฅ2 โ ๐ฅ + 2) b. ๐๐๐3(๐ฅ2 + 3) = ๐๐๐3(52)
c. ln (x + 2) + ln (3x โ 2) = 2 ln (2x) d. ๐๐๐3(7๐ฅ + 3) โ ๐๐๐3(๐ฅ + 1) = ๐๐๐3(2๐ฅ) e. log (x) + log (x โ 3) = log (28) f. ln (x - 5) + ln 4 = ln x - ln 2
โ Solving log equations in the form ๐๐๐๐(๐ฅ) = ๐
a. 3 + ๐๐๐9(4๐ฅ) = 5 b. 2 = โ3 + ln (๐ฅ + 2)
โ Solving log equations in the form ๐๐๐๐(๐ฅ) + ๐๐๐๐(๐ฆ) = ๐ or ๐๐๐๐(๐ฅ) โ ๐๐๐๐(๐ฆ) = ๐
Examples: Solve each equation for x. Round to the nearest hundredth. a. ๐๐๐12(12๐ฅ) + ๐๐๐12(๐ฅ โ 1) = 2 b. log (x โ 12 ) โ log (x โ 2 ) = 2
c. log (50x ) = 2 + log( 2x - 3 ) d. ๐๐๐1/4 (1
4๐ฅ) = โ
5
2 โ ๐๐๐1/4(๐ฅ + 8)