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

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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)

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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