Question 167361: Solve the following equation. Give exact answer to and a decimal aproximation to 2 decimal places of accuracy if needed.
3^(2x)-20=3^(x)
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Solve the following equation. Give exact answer to and a decimal aproximation to 2 decimal places of accuracy if needed.
3^(2x)-20=3^(x)
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Substitute y for 3^x
y^2 - 20 = y See that?
y^2 - y - 20 = 0
(y-5)*(y+4) = 0
y = 5, y = -4
Sub back 3^x for y
3^x = 5
x = log(5)/log(3) (exact)
x = 1.47 (2 decimals)
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3^x = -4 This is not possible, as no exponent of 3 will give a negative number (no real number will, there is a complex number that will).
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