`(log_(10) 500000- log_(10)5)` is equal to:

Options

A. 5
B. 50
C. 49995
D. 100000

Answer

To solve the expression \( \log_{10} 500000 - \log_{10} 5 \), we can use the properties of logarithms. Here’s the step-by-step solution:

### Step 1: Rewrite the first logarithm
We can express \( 500000 \) in terms of \( 5 \) and powers of \( 10 \):
\[ 500000 = 5 \times 10^5 \]

### Step 2: Apply the logarithm property
Using the logarithmic property \( \log_a(b \times c) = \log_a b + \log_a c \), we can rewrite the logarithm:
\[ \log_{10} 500000 = \log_{10} (5 \times 10^5) = \log_{10} 5 + \log_{10} (10^5) \]

### Step 3: Simplify the second logarithm
Now, we know that \( \log_{10} (10^5) = 5 \) because of the property \( \log_a (a^b) = b \):
\[ \log_{10} 500000 = \log_{10} 5 + 5 \]

### Step 4: Substitute back into the original expression
Now we substitute this back into the original expression:
\[ \log_{10} 500000 - \log_{10} 5 = (\log_{10} 5 + 5) - \log_{10} 5 \]

### Step 5: Cancel out the logarithms
The \( \log_{10} 5 \) terms cancel out:
\[ \log_{10} 500000 - \log_{10} 5 = 5 \]

### Final Answer
Thus, the final answer is:
\[ \boxed{5} \]