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PilotLPTM [1.2K]
3 years ago
15

Solve for e^2x-e^x=6

Mathematics
1 answer:
Brilliant_brown [7]3 years ago
5 0
e ^{2x} -e ^x=6
 ----(i)

Let, e ^x =t
Therefore, e^{2x} = t^{2}

Therefore, from (i),

t²-t=6 
t²-3t+2t-6=0
t(t-3)+2(t-3)=0

Therefore, (t-3)(t+2)=0
Therefore, t=3 or t = -2

But, 
e^x =t

Therefore, 

e^x = 3 or e^x = -2

Taking ln on both sides,
Therefore, 
ln(e^x)=ln(3) or ln(e^x) = ln(-2)

But natural log of negative numbers does not exist since negative numbers are not in the domain of ln(x)
Therefore, 
ln(e^x) = ln(-2) is discarded 
Therefore, x = ln(3) is the only solution.
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Answer:

  1. 109°, obtuse
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Step-by-step explanation:

You are exected to know the relationships of angles created where a transversal crosses parallel lines.

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The appearance of the diagram often gives you a clue.

You also expected to know the name (or category) of angles less than, equal to, or greater than 90°. Respectively, these are <em>acute</em>, <em>right</em>, and <em>obtuse</em> angles.

1. Adjacent angles are supplementary. The supplement of the given angle is 109°, so x will be obtuse.

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Answer:

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