Question

write as a single log show your work

log7m-(log7n+log7p)

Answer 1

i need the actual numbers

Answer 2

To combine the expression \( \log_7 m - (\log_7 n + \log_7 p) \), we can use the properties of logarithms.

**Step 1: Distribute the negative sign.**
\[
\log_7 m - \log_7 n - \log_7 p
\]

**Step 2: Use the property of logarithms that states \( \log_b a - \log_b c = \log_b \left( \frac{a}{c} \right) \).**
First, combine \( \log_7 m \) and \( \log_7 n \):
\[
\log_7 m - \log_7 n = \log_7 \left( \frac{m}{n} \right)
\]

**Step 3: Now combine that result with \( - \log_7 p \):**
\[
\log_7 \left( \frac{m}{n} \right) - \log_7 p = \log_7 \left( \frac{m/n}{p} \right) = \log_7 \left( \frac{m}{np} \right)
\]

Thus, the final result is:
\[
\log_7 \left( \frac{m}{np} \right)
\]

Answer 3

Sure, let's rewrite and solve the logarithmic expression you provided using specific numerical values.

Assume:

- \( m = 100 \)
- \( n = 10 \)
- \( p = 2 \)

Now we need to compute the expression:

\[
\log_7 m - (\log_7 n + \log_7 p)
\]

**Step 1: Calculate each logarithm individually.**

First, we need to find \( \log_7 100 \), \( \log_7 10 \), and \( \log_7 2 \).

Using the change of base formula:
\[
\log_b a = \frac{\log_k a}{\log_k b}
\]
we can calculate these values using base 10 or natural logarithms. For simplicity, I'll use base 10:

1. **Calculate \( \log_7 100 \)**:
\[
\log_7 100 = \frac{\log_{10} 100}{\log_{10} 7} = \frac{2}{\log_{10} 7} \approx \frac{2}{0.8451} \approx 2.36
\]

2. **Calculate \( \log_7 10 \)**:
\[
\log_7 10 = \frac{\log_{10} 10}{\log_{10} 7} = \frac{1}{\log_{10} 7} \approx \frac{1}{0.8451} \approx 1.18
\]

3. **Calculate \( \log_7 2 \)**:
\[
\log_7 2 = \frac{\log_{10} 2}{\log_{10} 7} \approx \frac{0.3010}{0.8451} \approx 0.35
\]

**Step 2: Plug these values back into the expression.**

Now we compute:
\[
\log_7 m - (\log_7 n + \log_7 p) = \log_7 100 - (\log_7 10 + \log_7 2)
\]

Substituting the numeric approximations:
\[
2.36 - (1.18 + 0.35) = 2.36 - 1.53 = 0.83
\]

**Final Result:**
The value of the expression \( \log_7 100 - (\log_7 10 + \log_7 2) \) is approximately:
\[
0.83
\]