Solve the equation for $$ x $$ $$ \begin{array}{c}\log _{3} 81=x \ x=[?]\end{array} $$

Question

UpStudy AI · Accepted Answer

To solve the equation:

$$
\log_{3} 81 = x
$$

We need to find the value of $$ x $$ such that $$ 3^x = 81 $$.

**Step 1: Rewrite the logarithmic equation in exponential form**

$$
3^x = 81
$$

**Step 2: Express 81 as a power of 3**

We know that:
$$
3^4 = 81
$$

**Step 3: Set the exponents equal to each other**

Since the bases are the same, the exponents must be equal:
$$
x = 4
$$

**Final Answer:**
$$
x = 4
$$
$$ x = 4 $$

Solve the equation for \( x \) \[ \begin{array}{c}\log _{3} 81=x \\ x=[?]\end{array} \]