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Solve for x given that 125^(x/2)=5

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stsf | Student, Grade 11 | eNoter

Posted September 5, 2011 at 6:51 AM via web

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Solve for x given that 125^(x/2)=5

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bluejay123 | Student, Grade 10 | eNoter

Posted September 5, 2011 at 7:29 AM (Answer #1)

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if the question is 125^(x/2)=5, then the question is the same as the square root of 125^x=5.  then you would square both sides which makes it 125^x=5^2. make the base equal the same, so that would make it 5^(3x)=5^2  so 3x=2 and x would be (2/3) 

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 5, 2011 at 12:31 PM (Answer #2)

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We have to solve for x given that 125^(x/2)=5

express 125^(x/2) as a power of 5

125^(x/2)

=> (5^3)^(x/2)

use the property x^a^b = x^(a*b)

=> 5^(3x/2)

As this is equal to 5 or 5^1, we can equate 1 and 3x/2

=> 3x/2 = 1

=> x = 2/3

The required value of x = 2/3

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