Ex 2.4 - Logarithmic Equations

1 2.5: Logarithmic equations Properties of logarithms: (1) log a mn  log a m  log a n m  log a m  log a n n (3) log a m n  n log a m

(2) log a

(4)log a b 

log c b log c a

Example 11 Solve the equation log2(x – 1) + log2(x + 3) - log2(x + 1) = 1 Example 12 Solve the equation log2

x + 2 log2 x – 2 = 0

Example 13 Solve the simultaneous equation:

log2(x – 4y) = 4 log84x – log8(8y + 5) = 1

Example 14 Solve the following logarithmic equations: (b) (a) log 3 N + log 9 N = 6

log 5 x = 4 log x5

Exercise 2.4: Logarithmic equations 1. Solve the following equations without using calculator. (a) lg 4 + 2 lg x = 2 (b) log2y2 = 3 + log2(y + 6) (c) lg y + lg (2y – 1) = 1 (d) loga7 + logax = 0 2. Without using calculator, solve (a) lg25 + lg x – lg(x – 1) = 2 (b) 2lg 3 + lg2x – lg(3x +1) = 0 (c) logy8 = ½ (d) 2log2y = 4 + log2(y + 5) (e) lg(x2 + 12x – 3) = 1 + 2lgx 3. Solve the simultaneous equations: (a) 3x = 9(27)y log27 – log2(11y – 2x) = 1 (b) lg x + 2lgy = 3 x2y = 125