LOGARITHMIC EQUATIONS-3

If Log₇(25x² - 10x + 50) = 2; find x.

solution

Log₇(25x² - 10x + 50) =2

25x² - 10x + 50 = 7² . 

25x² - 10x + 50 = 49 . 

25x² - 10x + 50 - 49 = 0 . 

25x² - 10x + 1 = 0 . 

We solve by factorization.

25x² - 10x + 1 = 0 . 

(25x² - 5x) - (5x + 1) = 0 . 

5x(5x - 1) - 1(5x - 1) = 0 . 

(5x - 1) (5x - 1) = 0 . 

so; 5x - 1 = 0 .  [since it is a perfect square]

5x =  1  .

5       5 

Hence x = ¹/₅

TRY THIS..................

NECTA 1997 QN8

If Log₃(x² - 4x + 76) = 4; find x.