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Chapter 12: Problem 2

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$3^{x}=81$$

Short Answer

Expert verified
The solution for the given exponential equation \(3^{x}=81\) is \(x=4\).

Step by step solution

01

Rewrite the Equation

In this step, express 81 as a power of 3: \(81=3^4\) . Therefore, the equation \(3^x=81\) can be written as \(3^x=3^4\).
02

Equate the Exponents

Since both sides of the equation have the same base, the exponents must be equal. Thus, we can write \(x=4\).
03

Verify the solution

Substitute \(x=4\) into the original equation. \(3^{x}=3^{4}\) equals to \(81=81\). This confirms that the solution is correct, as the left hand side equals the right hand side when \(x=4\).

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Most popular questions from this chapter

What question can be asked to help evaluate \(\log _{3} 81 ?\)

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