hi ppl. i'm not really sure how to do this question:
2lg5x - lg(1-x) = lg(4-x) + 1
it was from a assessment paper.
the answer is: x= 2/3 and x= -4
Thanks!!!
2lg5x - lg(1-x) = lg(4-x) + 1
lg (5x)² - lg (1-x) = lg (4-x) + lg 10
lg [25x²/(1-x)] = lg [(4-x)(10)]
25x²/(1-x) = 40 - 10x
25x² = 40 - 10x - 40x + 10x²
15x² + 50x - 40 = 0
3x² + 10x - 8 = 0
(3x - 2)(x + 4) = 0
x = 2/3 or x = -4
^ your solution is almost perfect.
however, you missed out a final and very important step.
can you find out where your mistake is?
they need to know about rejecting x = -4 as lg(5x) is not real for x = -4 ?