Question

Solve for $x$ algebraically. $$3^{x}=243$$

   Solve for $x$ algebraically.
$$3^{x}=243$$

Essentials of Precalculus

Essentials of Precalculus

Richard N. Aufmann,… 1st Edition

Chapter 3, Problem 2

Instant Answer

Solved by Expert Darshan Maheshwari

07/10/2021

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We need to express 243 as a power of 3. Show more…

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Solve for $x$ algebraically. $$3^{x}=243$$

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Key Concepts

Exponential Equations

Exponential equations are equations in which the variable is in the exponent. Solving these equations typically involves methods such as rewriting the equation so that both sides have the same base, or applying logarithms, in order to isolate and solve for the variable.

Conversion to a Common Base

This concept involves expressing each side of the equation as an exponent of the same base. Recognizing that different numbers can be represented as powers of a common base simplifies the process of comparing and solving exponential expressions.

Equality Property of Exponents

Once an equation is rewritten so that both sides have the same base, the equality property of exponents states that the exponents themselves must be equal. This property allows one to set up a simpler algebraic equation to solve for the unknown variable.

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