Question

Solve for $x$ in. $$\frac{1}{8^{x+1}}=16^{1-4 x}$$

   Solve for $x$ in.
$$\frac{1}{8^{x+1}}=16^{1-4 x}$$

Applied Calculus For Business, Economics, and Finance

Applied Calculus For Business, Economics, and Finance

Warren B. Gordon,…

Chapter 4, Problem 39

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Solved by Expert Bobby Barnes

03/10/2021

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$$8^{-x+1}=16^{1-4x}$$ Show more…

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Solve for $x$ in. $$\frac{1}{8^{x+1}}=16^{1-4 x}$$

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Key Concepts

Base Conversion

Base conversion is the process of rewriting different exponential expressions so that they share a common base. This technique is important in solving exponential equations because it enables the equating of exponents, which simplifies the process of isolating and solving for the unknown variable.

Exponential Equations

Exponential equations are mathematical statements that involve exponents where the variable in question appears in an exponent. Solving such equations typically involves rewriting the expressions so that both sides of the equation have the same base, allowing for the exponents to be set equal to each other and solved using algebraic techniques.

Properties of Exponents

The properties of exponents are a set of rules that govern how expressions with exponents are manipulated. These rules, such as the quotient of powers rule, power of a power rule, and change of base, are fundamental when rewriting exponential expressions, particularly when converting a complex expression into a more manageable form for solving equations.

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