Solve the exponential equation (e^(2x) - 10*e^x)/13 = 3.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The exponential equation: (e^(2x) - 10*e^x)/13 = 3 has to be solved

Let e^x = y

=> (y^2 - 10y) = 39

=> y^2 - 10y - 39 = 0

=> y^2 - 13y + 3y - 39 = 0

=> y(y - 13) + 3(y - 13) = 0

=> (y + 3)(y - 13) = 0

=> y = -3 and y = 13

But y = e^x which cannot be negative.

This leaves e^x = 13

=> x = ln 13

The solution of the equation (e^(2x) - 10*e^x)/13 = 3 is x = ln 13.

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