Solve e^(.5ln(.25(x^2 + 4))) = 1  

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We have to solve e^(0.5*ln(.25(x^2 + 4))) = 1

e^(0.5*ln(0.25(x^2 + 4))) = 1

use the property that a*log b = log b^a

e^(ln(0.25(x^2 + 4))^(0.5)) = 1

e^ln a = a as ln represents logarithm to the base e

0.5*(x^2 + 4)^(0.5) = 1

=> sqrt (x^2 + 4) = 2

=> x^2 + 4 = 4

=> x^2  = 0

=> x = 0

The required solution is x = 0

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