Question

Solve for the unknown. $2^{x^{2}-2 x}=8$

   Solve for the unknown.
$2^{x^{2}-2 x}=8$

Calculus for AP

Calculus for AP

Jon Rogawski & Ray… 2nd Edition

Chapter 1, Problem 31

Instant Answer

Solved by Expert Natalie Anderson

03/17/2020

Step 1

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

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Solve for the unknown. $2^{x^{2}-2 x}=8$

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Key Concepts

Exponential Equations

Exponential equations are those in which the variable appears in the exponent. Solving these equations often involves methods to rewrite or manipulate the exponents so that either the bases become the same or logarithmic techniques can be applied to isolate the variable.

Rewriting Terms with Common Bases

Rewriting numbers as powers of a common base is a key method for solving exponential equations. It allows the equation to be transformed so that both sides have the same base, which then permits the equating of the exponents.

Equating Exponents

When two expressions with the same positive base (other than 1) are equal, the exponents must also be equal. This principle simplifies solving exponential equations by reducing the problem to setting the exponents equal to each other.

Quadratic Equations

After equating the exponents, the resulting equation may be a quadratic equation. Quadratic equations, which are polynomial equations of degree two, can be solved using methods such as factoring, the quadratic formula, or completing the square, making them a fundamental part of algebra.

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