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Solve for x.
12^(sqrt{x^2}) - 24^(x - 2) = 144
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It is not for algebraic solution - in Algebra, there are no methods solving such equations.
Use either your graphics calculator or online tools to get approximate numerical solutions.
For example, you may use an online solver https://www.desmos.com/calculator
Print there y = 12^(sqrt{x^2}) - 24^(x - 2) in one window and y = 144 in another window.
Calculator will provide the plot, and you can identify two root
x = -2 (an approximate value) and x = 2.00281 (another approximate value)
by clicking at the intersection points. ANSWER
Solved.