Question

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

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

Elementary and Intermediate Algebra

Elementary and Intermediate Algebra

Alan S. Tussy, R.… 5th Edition

Chapter 11, Problem 25

Instant Answer

Solved by Expert Heather Zimmers

04/07/2020

Step 1

Since 8 is $2^{3}$, we can rewrite the equation as: $$2^{x^{2}-2 x}=2^{3}$$ Show more…

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

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Key Concepts

Exponential Equations

Exponential equations involve variables in exponents and require techniques that often include rewriting the equation so that both sides share the same base. This makes it possible to set the exponents equal to each other and simplifies the solution process.

Equating Exponents with a Common Base

When both sides of an exponential equation can be expressed with the same positive base (other than 1), the equality of the entire expressions implies that the exponents themselves must be equal. This is a key step in reducing the problem to a simpler algebraic equation.

Quadratic Equations

A quadratic equation is a second-degree polynomial equation of the form ax^2 + bx + c = 0. When an exponential equation is reduced by equating exponents, the resulting equation may be quadratic, which can then be solved using factoring, the quadratic formula, or other methods appropriate for quadratic equations.

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