Question

Solve each equation. $$ 2^{x^{2}-2 x}=8 $$

   Solve each equation.
$$
2^{x^{2}-2 x}=8
$$

Intermediate Algebra

Intermediate Algebra

Alan S. Tussy, R.… 5th Edition

Chapter 9, Problem 25

Instant Answer

Solved by Expert Heather Zimmers

08/01/2020

Step 1

We know that $8$ can be written as $2^3$. So, the equation becomes: $$2^{x^{2}-2 x}=2^3$$ Show more…

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Solve each equation. $$ 2^{x^{2}-2 x}=8 $$

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Key Concepts

Quadratic Equations

Quadratic equations are polynomial equations of degree two. In the context of exponential equations, equating exponents can yield a quadratic equation. Standard methods such as factoring, completing the square, or using the quadratic formula are then applied to find the variable’s values.

Equating Exponents

Once both sides of an exponential equation are expressed with the same base, the property of exponentials establishes that the exponents must be equal. This transforms the original exponential equation into an algebraic equation, which is generally easier to solve.

Base Conversion

Base conversion involves rewriting numbers to express them as powers of a common base. This step is crucial when solving exponential equations because it allows one to equate exponents directly by ensuring both sides of the equation have the same base.

Exponential Equations

Exponential equations are equations where the variable appears in the exponent. Solving these typically requires manipulation to isolate the exponential term or to rewrite the equation so that both sides have the same base, enabling further simplification.

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