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How to use the property of exponentials of being injective, in an equation?How to use...

portoruj | Student, Grade 10 | eNoter

Posted April 11, 2011 at 5:36 AM via web

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How to use the property of exponentials of being injective, in an equation?

How to use the property of exponentials of being injective, in an equation?

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giorgiana1976 | College Teacher | Valedictorian

Posted April 11, 2011 at 12:04 PM (Answer #2)

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Here's an example:

4^(x-1) = 8*2^3x , x = ?

Since 8 is a power of 2, we'll write it as:

8  =2^3

Now, we'll apply the multiplication rule of 2 exponentials that have matching bases:

2^3*2^3x = 2^(3 + 3x)

We'll re-write the equation, putting 4 = 2^2

2^2(x-1) = 2^(3 + 3x)

Since the bases are matching, we'll apply one to one rule:

2(x-1) = (3 + 3x)

We'll open the brackets:

2x - 2 = 3x + 3

We'll subtract 2x - 2 and we'll apply symmetrical property:

3x + 3 - 2x + 2 = 0

x + 5 = 0

We'll subtract 5:

x = -5

The solution of the equation is x = -5.