Sum of a Triple

Algebra Level 4

a,ba, b and cc are positive real numbers greater than or equal to 1 satisfying

abc=100,algablgbclgc10000. \begin{aligned} abc & =100,\\ a^{\lg a} b^{\lg b} c^{\lg c} & \geq 10000. \\ \end{aligned}

What is the value of a+b+ca + b + c ?

Details and assumptions:

  • lg\lg refers to log base 10.

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