Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Jan 05, 2024

Solve the exponential equation $3^{x}=81$ .

STEP 1

Assumptions
1. We are given the equation $3^{x} = 81$ .
2. We need to solve for the value of $x$ .

STEP 2

Recognize that $81$ is a power of $3$ , since $81 = 3^4$ .

STEP 3

Rewrite the equation using $81$ as a power of $3$ .
$3^{x} = 3^4$

STEP 4

Since the bases are the same and the equation states that the two expressions are equal, the exponents must also be equal.

STEP 5

Set the exponents equal to each other to solve for $x$ .
$x = 4$
The solution to the equation $3^{x} = 81$ is $x = 4$ .

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