If `0.42xx100^(k)=42`, then the value of k is

Options

A. 4
B. 2
C. 1
D. 3

Answer

To solve the equation \(0.42 \times 100^k = 42\), we can follow these steps:

### Step 1: Isolate \(100^k\)
We start by dividing both sides of the equation by \(0.42\):

\[ 100^k = \frac{42}{0.42} \]

### Step 2: Simplify the right side
Next, we simplify \(\frac{42}{0.42}\):

\[ \frac{42}{0.42} = 100 \]

This gives us:

\[ 100^k = 100 \]

### Step 3: Rewrite \(100\) as a power of \(100\)
We can express \(100\) as \(100^1\):

\[ 100^k = 100^1 \]

### Step 4: Set the exponents equal to each other
Since the bases are the same, we can set the exponents equal to each other:

\[ k = 1 \]

### Conclusion
Thus, the value of \(k\) is:

\[ \boxed{1} \]