If `10^x=1.73` and `log_(10) 1730=3.2380` then `x` is equal to

Options

A. 1.238
B. 0.238
C. 2.38
D. 2.238

Answer

To solve the equation \(10^x = 1.73\) and find the value of \(x\), we can follow these steps:

### Step 1: Rewrite the equation
We start with the equation:
\[ 10^x = 1.73 \]

### Step 2: Multiply both sides by 1000
To relate \(1.73\) to \(1730\), we can multiply both sides by \(1000\):
\[ 10^x \times 1000 = 1.73 \times 1000 \]
This simplifies to:
\[ 10^x \times 10^3 = 1730 \]

### Step 3: Combine the powers of 10
Since \(10^x \times 10^3\) can be combined as:
\[ 10^{x + 3} = 1730 \]

### Step 4: Take the logarithm of both sides
Now, we take the logarithm (base 10) of both sides:
\[ \log_{10}(10^{x + 3}) = \log_{10}(1730) \]

### Step 5: Apply the logarithmic identity
Using the property of logarithms that states \(\log_{10}(10^a) = a\), we can simplify the left side:
\[ x + 3 = \log_{10}(1730) \]

### Step 6: Substitute the known value of the logarithm
We know from the problem statement that:
\[ \log_{10}(1730) = 3.2380 \]
Substituting this value in gives us:
\[ x + 3 = 3.2380 \]

### Step 7: Solve for \(x\)
To isolate \(x\), we subtract \(3\) from both sides:
\[ x = 3.2380 - 3 \]
This simplifies to:
\[ x = 0.2380 \]

### Final Answer
Thus, the value of \(x\) is:
\[ \boxed{0.2380} \]