To solve this equation, we can use the following steps:
Isolate the x term on one side of the equation. To do this, we can subtract 100x^logx from both sides: x^1+2logx - 100x^logx = 0
Simplify the left side of the equation by using the rule for adding exponents with the same base: x^(1+2logx) - 100x^logx = 0
Use the rule for multiplying exponents with the same base to simplify the right side of the equation: x^(1+2logx) = 100x^logx
Solve for x by dividing both sides of the equation by x^logx: x^(1+2logx)/x^logx = 100
Use the rule for dividing exponents with the same base to simplify the left side of the equation: x^(1/x) = 100
Take the x^(1/x)th root of both sides to solve for x: x = 10
Therefore, the solution to the equation is x = 10.
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