Certainly! Let's solve the expression \(\frac{15.05 \times \sqrt{0.00695}}{6.95 \times 10^2}\) using logarithms.
We start with the expression:
[tex]\[ \frac{15.05 \times \sqrt{0.00695}}{6.95 \times 100} \][/tex]
First, let's denote the numerator and denominator individually:
[tex]\[ \text{Numerator} = 15.05 \times \sqrt{0.00695} \][/tex]
[tex]\[ \text{Denominator} = 6.95 \times 100 \][/tex]
Now, we need to evaluate both parts step by step.
### Step 1: Evaluate the Numerator
The numerator is:
[tex]\[ 15.05 \times \sqrt{0.00695} \][/tex]
First, find \(\sqrt{0.00695}\):
[tex]\[ \sqrt{0.00695} \approx 0.0833516 \][/tex]
Now multiply by 15.05:
[tex]\[ 15.05 \times 0.0833516 \approx 1.254668 \][/tex]
So, the value of the numerator is approximately:
[tex]\[ 1.254668 \][/tex]
### Step 2: Evaluate the Denominator
The denominator is:
[tex]\[ 6.95 \times 100 = 695 \][/tex]
So, the value of the denominator is:
[tex]\[ 695 \][/tex]
### Step 3: Combine the Numerator and Denominator
Finally, we combine the results from Steps 1 and 2 to get the fraction:
[tex]\[ \frac{1.254668}{695} \][/tex]
Now, perform the division:
[tex]\[ \frac{1.254668}{695} \approx 0.001806 \][/tex]
Thus, the evaluated expression is approximately:
[tex]\[ 0.001805278 \][/tex]
### Summary
Let's summarize the result:
- Numerator: \(1.254668\)
- Denominator: \(695\)
- Final Value: \(0.001805278\)
The evaluated result of the expression \(\frac{15.05 \times \sqrt{0.00695}}{6.95 \times 10^2}\) is:
[tex]\[ \boxed{ 0.001805278 } \][/tex]
