Solve the exponential equations exactly for $x$. $$5^{x^{2}-3}=5^{2 x}$$
Added by Nicole B.
Step 1
We want to find the value(s) of $x$ that make this equation true. Since $5^0 = 1$ for any base, we can see that the equation is true when the exponent is 0: $$x^2-3-2x = 0$$ This is a quadratic equation that we can solve using the quadratic formula: $$x = Show more…
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