The solution set of the equation 4log9 x-6.xlog9 2 + 8 = 0 is ______.
Mostafijur Rahaman , 10 Years ago
Grade 12
Algebra> The solution set of the equation 4 log 9 ...
2 Answers
Y RAJYALAKSHMI
Last Activity: 10 Years ago
We have xlogay = ylogax
S, xlog92 = 2log9x
4log9 x -6.xlog9 2 + 8 = 0
=> (22)log9x – 6. 2log9x + 8 = 0
=> (2log9x )2 - 6. 2log9x + 8 = 0
let 2log9x = y
Then, the given equation becomes, y2 – 6y + 8 = 0 and the solution is y = 4 & 2
when y = 4, 2log9x = 22 => log9x = 2 => x = 92 = 81
when y = 2, 2log9x = 2 => log9x = 1 => x = 9
Ans: Solution set = {9, 81}
Mostafijur Rahaman
Last Activity: 10 Years ago
thnx
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