Question

Solve for $x$ in. $$8^{2 x-3}=16^{1-4 x}$$

   Solve for $x$ in.
$$8^{2 x-3}=16^{1-4 x}$$

Applied Calculus For Business, Economics, and Finance

Applied Calculus For Business, Economics, and Finance

Warren B. Gordon,…

Chapter 4, Problem 38

Instant Answer

Solved by Expert Bobby Barnes

03/10/2021

Step 1

Since 8 and 16 can both be expressed as powers of 2, we rewrite 8 as $2^3$ and 16 as $2^4$. The equation becomes: $$(2^3)^{2x-3} = (2^4)^{1-4x}$$ Show more…

Show all steps

lock

Thanks for your feedback!

Solve for $x$ in. $$8^{2 x-3}=16^{1-4 x}$$

Play audio

Feedback

Powered by NumerAI

Bobby Barnes and 74 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Exponentiation

Exponentiation is a mathematical operation involving a base and an exponent, where the base is multiplied by itself as many times as indicated by the exponent. This concept is crucial for understanding equations where variables appear in exponents.

Rewriting to a Common Base

When solving exponential equations, it is often beneficial to express all terms with the same base. This allows the use of exponent laws to simplify the equation by comparing the exponents directly.

Equating Exponents

Once both sides of an exponential equation have the same base, the one-to-one property of exponential functions allows us to set the exponents equal to each other. This transforms the original equation into a simpler, usually linear, equation.

Solving Linear Equations

After equating the exponents, the problem reduces to solving a linear equation in one variable. This involves standard techniques such as combining like terms and isolating the variable to determine its value.

Recommended Videos

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later