Brook L.

asked • 02/05/18

7=(1/3)^2x-1 What does x equal

Solve for x

Arturo O.

Student,
 
Do you mean
 
7 = (1/3)2x - 1
 
or
 
7 = (1/3)2x-1
 
?
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02/05/18

Brook L.

7 = (1/3)2x-1 Sorry that I didn't state it clearly.
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02/05/18

1 Expert Answer

By:

Karyn T. answered • 02/05/18

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Not sure if you have worked with logarithms yet but logs undo exponents. Logs and exponents are inverses of each other.
Take the log base 10 of both sides of the equation.....log7 = (2x-1)log(1/3), then simplify.
2x-1 = log7/log(1/3). The log of a number is just a value. Try log7 on your calculator to see what value you get.
or x = [log7/log(1/3) + 1]/2      x = -0.386
 
Another approach using a change of bases..... log1/37 = 2x-1, x = -0.386
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Kenneth S.

Karyn, isn't it best to get the clarification requested by Arturo before working this problem?
 
Brook, here are some parentheses which you can use to clarify the problem:  ((  ))
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02/05/18

Brook L.

7=(1/3)(2x-1)
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02/05/18

Brook L.

Thank you!
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02/05/18

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