How do I solve this? List all solutions to the equation (9 to the power x) - [3 to the power (x+1)] = 10.? - reviews of 10 power compact binoculars
I have not studied mathematics for over a year and are in desperate need of revision.
Thursday, February 4, 2010
Reviews Of 10 Power Compact Binoculars How Do I Solve This? List All Solutions To The Equation (9 To The Power X) - [3 To The Power (x+1)] = 10.?
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9 = x ^ (3 ^ 2) = x ^ 3 ^ (2x) = (3 ^ x) ²
3 ^ (x +1) = x ^ 3 * 3 ^ 1 = 3 * 3 ^
His problem is equivalent to
(3 ^ x) ² - 3 * 3 ^ x = 10
(3 ^ x) ² - 3 * 3 ^ x - 10 = 0
Y = 3 ^ x. Then this equation can be written
y ² - 3y - 10 = 0
Factor (or use) the quadratic formula:
(y - 5) (y + 2) = 0
y = 5 or y = -2
Thus, in terms of x, we
y = 3 x = 5
or
y = 3 x = -2
It has no real solution (3 x ^> 0 for all real x) and so we stayed with
3 ^ x = 5
Take the log (no legitimate basis) of both sides:
log (3 ^ x) = log (5)
With the law on registration
log (a ^ b) = log b (a)
we can write the
x log (3) = log (5)
⇒ x = log (5) / log (3) ≈ 1465
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