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

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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?

Posted by portoruj on April 11, 2011 at 5:36 AM via web and tagged with discussion, math

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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.

Posted by giorgiana1976 on April 11, 2011 at 12:04 PM (Answer #2)