Question

(e^x)^x*e^24=e^12x
solve

Answer 1

(e^x)^x = e^(x^2)
e^(x^2) * e^24 = e^(x^2 + 24)
Therefore, e^(x^2 + 24) = e^(12x)
Take the ln of both sides:
\[\ln(e ^{x ^{2}+24}) =\ln(e ^{12x}) \rightarrow x ^{2} + 24 = 12x \rightarrow x ^{2} -12x + 24 = 0\]
Use quadratic equation: (-b +- sqrt(b^2 - 4ac))/2a
(-(-12) +/- sqrt(144 - 4(1)(24))/2
= (12 + sqrt(144-96))/2 = 6+sqrt(48)/2 = 6 + 2sqrt(3)
Other x = 6 - 2sqrt(3)