math grade 12....help me!?

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27(3^2x) -242(3^x) - 9 = 0

2007-10-14 12:24:57 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics

Let 3^x = z, so

27z^2 -242z - 9 = 0, so

(27z + 1)(z - 9) = 0, so

27z = -1, or z = 9.

Now solve for z.

2007-10-14 13:02:12 · answer #1 · answered by Twiggy 7 · 0⤊ 0⤋

call 3^x = z
so 27 z^2-24z-9=0
9z^2-8z-3=0
z= ((8+-sqrt(64+108))/18 z>0
z=(4+sqrt(43))/9 and x= [log((4+sqrt43)/9]/log3

2007-10-14 12:38:14 · answer #2 · answered by santmann2002 7 · 0⤊ 1⤋