Look at the figure. Find the value of x.
2 answers:
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Answer:
x = 1
Step-by-step explanation:
3^2x - 9 (3^-2x) = 8
<=> 3^2x - 9/(3^2x) = 8
Given that 3^2x = y [1] (y>0), we have a new equation as follows:
y - 9× = 8
<=> y - 9/y = 8
<=> y(y - 9/y) = y×8
<=> y^2 - 9 = 8×y
<=> y^2 - 8y - 9 = 0
<=> (y^2 + y) - (9×y + 9) = 0
<=> y(y + 1) - 9(y + 1) = 0
<=> (y - 9)(y + 1) = 0
=> y = 9, or y = - 1
However, as 3^2x > 0, y>0.
Therefore, y = 9.
Replace y with 9 in [1], we have:
3^2x = 9 = 3^2
=> 2x = 2
=> x = 1