Solve for x in. 2^5 x=8^3 x+1

Name: Problem 37, Chapter 4: Applied Calculus For Business, Economics, and Finance
Uploaded: 2021-03-10T22:21:52-08:00
Duration: 1 min 4 s
Channel: Bobby Barnes
Description: Solve for x in. 2^5 x=8^3 x+1

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Key Concepts

Properties of Exponents

Properties of exponents include rules such as multiplying powers with the same base, raising a power to a power, and converting radical expressions to exponential form. These rules are essential when simplifying and rewriting exponential expressions during the solution process.

Base Conversion

Base conversion involves rewriting expressions so that they share a common base. This is particularly useful when one side of the equation has an exponent based on a more complex base that can be expressed as a power of a simpler base, enabling the comparison of exponents directly.

Exponential Equations

Exponential equations involve variables in the exponent. Solving these equations typically requires manipulating the expressions so that the exponential functions have the same base, allowing the exponents to be compared directly. This forms the foundation for finding the variable in the exponent.

Equating Exponents

Once the exponential expressions on both sides of an equation have the same base, the exponents themselves can be equated. This step transforms an exponential equation into a simpler linear or polynomial equation that is much easier to solve.

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