the value of x when `log_(x) 343=3`,is

Options

A. 7
B. 8
C. 3
D. 27

Explanation

To solve the equation \( \log_{x} 343 = 3 \), we can follow these steps:

### Step 1: Rewrite the logarithmic equation in exponential form
The equation \( \log_{x} 343 = 3 \) can be rewritten using the definition of logarithms. This means that:
\[ x^3 = 343 \]

**Hint:** Remember that \( \log_{b}(a) = c \) implies \( b^c = a \).

### Step 2: Solve for \( x \)
Now we need to find \( x \) by taking the cube root of both sides of the equation:
\[ x = \sqrt[3]{343} \]

**Hint:** To find the cube root, think about what number multiplied by itself three times equals 343.

### Step 3: Simplify \( 343 \)
Next, we can simplify \( 343 \). We can express \( 343 \) as:
\[ 343 = 7^3 \]

**Hint:** Try to factor \( 343 \) into prime factors to see if it can be expressed as a power of a smaller number.

### Step 4: Substitute back into the equation
Now, substituting back, we have:
\[ x = \sqrt[3]{7^3} \]

**Hint:** Recall that the cube root of a power can simplify the expression.

### Step 5: Simplify further
Using the property of exponents, we can simplify this to:
\[ x = 7 \]

**Hint:** When taking the cube root of a power, the exponents can be divided.

### Conclusion
Thus, the value of \( x \) is:
\[ \boxed{7} \]