Question

Solve the equation. $$2^{x}-10\left(2^{-x}\right)+3=0$$

   Solve the equation.
$$2^{x}-10\left(2^{-x}\right)+3=0$$

College Algebra

College Algebra

James Stewart,… 7th Edition

Chapter 4, Problem 44

Instant Answer

Solved by Expert Ankit Gupta

07/24/2020

Step 1

The equation becomes: $$y - 10\left(\frac{1}{y}\right) + 3 = 0$$ Show more…

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Solve the equation. $$2^{x}-10\left(2^{-x}\right)+3=0$$

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Key Concepts

Properties of Exponents

A solid understanding of the properties of exponents is essential when dealing with exponential equations. These properties, such as the rule a^(-x) = 1/(a^x), are used to rewrite and simplify terms, thereby facilitating the transformation and solution of equations where the variable appears in the exponent.

Quadratic Equations

Quadratic equations, which are second-degree polynomial equations, can typically be solved using methods like factoring, completing the square, or the quadratic formula. Transforming an exponential equation into a quadratic form allows the application of these well-known solving techniques.

Substitution Method

The substitution method is a powerful technique where a complicated expression is replaced by a single variable to simplify the equation. This is particularly useful in transforming exponential equations into polynomial equations, such as quadratics, which are easier to solve.

Exponential Equations

Exponential equations involve variables in the exponent and require specialized techniques for their solution. These equations often necessitate the use of properties of exponents or logarithms to isolate the variable present in the exponent.

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