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Solve. 16^x=8 | Numerade

Name: Problem 23, Chapter 12: Algebra A Combined Function
Uploaded: 2022-02-15T13:24:28-08:00
Duration: 1 min 31 s
Channel: Gregory Higby
Description: Solve. 16^x=8

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Key Concepts

Exponential Equations

Exponential equations are equations where the unknown variable appears in the exponent. Solving these equations often involves rewriting the terms so that both sides of the equation have the same base, which then allows the use of properties of exponents to equate the exponents directly.

Rewriting Expressions to Have a Common Base

Rewriting expressions to have a common base involves expressing different exponential terms with the same base. This technique simplifies the process by allowing the comparison of exponents directly, using the principle that if two powers with the same base are equal, then their exponents must also be equal.

Properties of Exponents

The properties of exponents, such as the power of a power rule (i.e., (a^m)^n = a^(m*n)), facilitate the manipulation of exponential expressions. These rules are crucial for simplifying exponential equations, especially when converting terms into a form where a common base can be identified.

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