Daniel L.

asked • 03/23/15

22.97=-1.34^-n

Trying too find n. I think this would involve natural log, but I'm confused since there's a negative.

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Mark M. answered • 03/24/15

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An exponent applies only to the symbol (immediate) upon which it sits.
 
22.97 = -1.34-n, the leading negative on the 1.34 is not included in the exponentiation (if it did it would be (-1.34)-n)
-22.97 = 1.34-n
 
Getting a negative number (-22.97) from the exponentiation of a positive number (1.34) is not possible.  
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Michael J. answered • 03/24/15

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We will use the log.
 
 
Log both sides of equation.
 
Log 22.97 = Log 1.34-n
 
 
Bring the exponent -n as the coefficient of the log.
 
Log 22.97 = -nLog 1.34
 
 
Divide both sides of equation by Log 1.34
 
(Log 22.97) / (Log 1.34) = -n
10.709 = -n
 
-10.709 = n
 
 
 
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Michael J.

Please disregard this solution.  I did not take into account of the negative sign in front of the 1.34.  I will post the actual solution as soon as I figure this out.
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03/24/15

Michael J.

Okay. I figured something out. When we use logs, we will have
 
(Log 22.97) / (Log -1.34) = -n
 
Let's separate the logs into their own functions.
 
Log 22.97 = x            and        Log -1.34 = y
 
                            becomes
 
10x = 22.97               and         10y = -1.34
 
 
We will find x and y.  Then divide x by y to obtain -n.
 
Notice that when we raise 10 to a positive power, we will have a positive number greater than 1.  When we raise 10 to a negative power, we will have a positive number less than 1. 
 
An example:
 
(10)2 = 100
(10)-2 = 0.01
 
The results are both positive.
 
This means the result will never be a negative value.  So, for  10y = -1.34 ,  there is no y value that will give you a negative number and will not be able to solve for our -n.
 
You mentioned that you wanted to use natural log.  That will not work because your base number will be e instead of 10.  Both base numbers are positive.  It will be the same scenario.
 
Therefore, there is no solution to this problem.
 
 
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03/24/15

Harvey F.

Michael J.
When you enter your original solution into the original problem, it checks just fine.
1.34^(-(-10.709)) = 22.97
so n =-10.709
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03/24/15

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