Find the value of $$ x $$ : $$ \begin{array}{c}\log _{3} x=5 \ x=[?]\end{array} $$

Question

UpStudy AI · Accepted Answer

To solve for $$ x $$ in the equation:

$$
\log_{3} x = 5
$$

we can follow these steps:

### Step 1: Understand the Logarithmic Equation
The equation $$ \log_{3} x = 5 $$ asks the question: "To what power must we raise 3 to obtain $$ x $$?"

### Step 2: Rewrite the Equation in Exponential Form
A logarithmic equation $$ \log_{b} a = c $$ is equivalent to the exponential equation $$ b^{c} = a $$.

Applying this to our equation:
$$
\log_{3} x = 5 \quad \Rightarrow \quad 3^{5} = x
$$

### Step 3: Calculate $$ 3^{5} $$
$$
3^{5} = 3 \times 3 \times 3 \times 3 \times 3 = 243
$$

### Step 4: Conclusion
$$
x = 243
$$

**Answer:** $$ x = 243 $$
$$ x = 243 $$

Find the value of \( x \) : \[ \begin{array}{c}\log _{3} x=5 \\ x=[?]\end{array} \]

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