Solve the equation. $$ 3^{x}=243 $$

1. Express $$243$$ as a power of $$3$$: We have \[ 243=3^5. \] 2. Substitute into the equation: \[ 3^x=3^5. \] 3. Since the bases are equal, the exponents must be equal: \[ x=5. \] $$ x = 5 $$

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Premium

Home Question Bank Math Algebra

Question

Solve the equation.

Ask by Cervantes Ortega. in the United States

Mar 25,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

Solution

Express as a power of :
We have
Substitute into the equation:
Since the bases are equal, the exponents must be equal:

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg

Explain

Simplify this solution

The Deep Dive

To solve the equation

, we first recognize that 243 can be expressed as a power of 3. Specifically,

. Therefore, we can rewrite the equation as:

Since the bases are the same, we can set the exponents equal to each other:

Thus, the solution to the equation

Now you know how to leverage exponential expressions! It’s pretty neat when numbers can reveal their relationships in such an elegant way. If you ever encounter a similar situation, just find the common base, and you’re golden!

Moreover, keep in mind that practice makes perfect! Solving more equations like these will definitely sharpen your skills and make you a pro at tackling exponents.

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