Question

Match each solution to the equation

A. Log 10^2
B. Log 1000
C. 10^log 1000
D. 10^log x =100 x=

2
3
100
10^3
10000
4
10

Answer 1

To match each solution to the given equations, we first need to evaluate each option:

A. **Log 10^2**: This can be simplified using the property of logarithms.
\[
\text{Log} \, 10^2 = 2 \cdot \text{Log} \, 10 = 2 \cdot 1 = 2.
\]

B. **Log 1000**: We convert 1000 to a power of 10:
\[
1000 = 10^3 \implies \text{Log} \, 1000 = \text{Log} \, 10^3 = 3 \cdot \text{Log} \, 10 = 3 \cdot 1 = 3.
\]

C. **10^log 1000**: Using the change of base property,
\[
\text{Log} \, 1000 = 3 \implies 10^{\text{Log} \, 1000} = 10^3 = 1000.
\]

D. **10^log x = 100**: Here, we want to find the value of x:
\[
10^{\text{Log} \, x} = 100 = 10^2 \implies \text{Log} \, x = 2 \implies x = 10^2 = 100.
\]

Now, summarizing the results of each option, we have:
- A → 2
- B → 3
- C → 1000
- D → 100

Thus, the matching solutions are:
- A = 2
- B = 3
- C = 1000
- D = 100

The final answers for matching:
- **A** → **2**
- **B** → **3**
- **C** → **1000**
- **D** → **100**