## Exponential equation

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
winkylocc
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Joined: Thu Mar 31, 2011 3:19 am
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### Exponential equation

I have a problem I'm posting here. I already have the answer that Im posting as well along with the steps that the instructor wrote next to my incorrect answer. I need help with one of the steps that completely lost me.
Here is the problem:

5 2x+1 = 7 3-x

The steps follow:

2x+1 = (3-x) log 5 7
What he does next with the (3-x) is what really throws me:
2x+1 = 3 log5 7 - x log 5 7

2x + x log 5 7 = 3 log 5 7 - 1

x(2 + log 5 7) = 3 log 5 7 - 1

The answer is:

x = 3 log 5 7 -1
• 2 + log 5 7
Again, I was with him until the right side of the second step where things started happening that I cant figure out. Thanks for the help.

stapel_eliz
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Joined: Mon Dec 08, 2008 4:22 pm
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5 2x+1 = 7 3-x

2x+1 = (3-x) log 5 7

What he does next with the (3-x) is what really throws me:

2x+1 = 3 log5 7 - x log 5 7
He just distributed, like this:

. . . . .(3 - x)y = 3(y) - x(y) = 3y - xy

winkylocc
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Joined: Thu Mar 31, 2011 3:19 am
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### Re: Exponential equation

How will I know to distribute in a problem like that.

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
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How will I know to distribute in a problem like that.
Sometimes distributing is helpful; sometimes factoring is helpful. In general, use the step(s) you need for isolating the variable.

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