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Solving Exponential Equations Problem 1.2 (complexity 2). Solution

Solve

Solution
We can write the equation as
This last equation can be interpreted as a quadratic equation in .
Using the quadratic formula to solve for yields
But since an exponential function is always positive, we must reject the negative number. By observing that
we have the same base on both sides of the equation.
Since an exponential function is a one-to-one function, we can equate exponents:

Answer:

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