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this is from the 1990 mu alpha theta competition a is not equal to one and we know that the eighth root of 10 000 in base a is equal to 10 base a so what is a remember how our place value system works ten base a is one copy of a to the one plus no copies of a to the zero together thatamp;#39;s a similarly the thing under the root ten thousand base a is one a to the four plus zero a bunch of other things so in total itamp;#39;s a to the power of four thus replacing ten thousand base a with a to the four and 10 base a with a we arrive at this equation and that means that a to the 4 over a equals a to the 1 so 4 over a equals 1 hence a must be equal to 4.