3=log(4)(x^2+15)

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You appear to be using Log base 10.  Divide both sides by log(4) Now you have 4.98289 = x^2 +15 This leads to x^2 = -10.171 which does not have a real number solution because no number multiplied by itself is negative. Its x = + or - iSQR(10.171) or (+ or - ) 3.16498 i.